16 the multiplier method for simplifying complex fractions
TRANSCRIPT
![Page 1: 16 the multiplier method for simplifying complex fractions](https://reader035.vdocuments.mx/reader035/viewer/2022062515/55cfa04bbb61eb503f8b4692/html5/thumbnails/1.jpg)
Complex Fractions
Frank Ma © 2011
![Page 2: 16 the multiplier method for simplifying complex fractions](https://reader035.vdocuments.mx/reader035/viewer/2022062515/55cfa04bbb61eb503f8b4692/html5/thumbnails/2.jpg)
Complex FractionsA fraction with its numerator or the denominator containing fraction(s) is called a complex fraction.
![Page 3: 16 the multiplier method for simplifying complex fractions](https://reader035.vdocuments.mx/reader035/viewer/2022062515/55cfa04bbb61eb503f8b4692/html5/thumbnails/3.jpg)
Complex FractionsA fraction with its numerator or the denominator containing fraction(s) is called a complex fraction. In other words, a complex fraction is a fractional expression divided by another fractional expression.
![Page 4: 16 the multiplier method for simplifying complex fractions](https://reader035.vdocuments.mx/reader035/viewer/2022062515/55cfa04bbb61eb503f8b4692/html5/thumbnails/4.jpg)
Complex FractionsA fraction with its numerator or the denominator containing fraction(s) is called a complex fraction. In other words, a complex fraction is a fractional expression divided by another fractional expression.We want to simplify complex fractions to regular fractions.
![Page 5: 16 the multiplier method for simplifying complex fractions](https://reader035.vdocuments.mx/reader035/viewer/2022062515/55cfa04bbb61eb503f8b4692/html5/thumbnails/5.jpg)
Complex FractionsA fraction with its numerator or the denominator containing fraction(s) is called a complex fraction. In other words, a complex fraction is a fractional expression divided by another fractional expression.We want to simplify complex fractions to regular fractions.The “easy” complex fractions are just regular divisions of of a fraction by another fraction.
![Page 6: 16 the multiplier method for simplifying complex fractions](https://reader035.vdocuments.mx/reader035/viewer/2022062515/55cfa04bbb61eb503f8b4692/html5/thumbnails/6.jpg)
Complex FractionsA fraction with its numerator or the denominator containing fraction(s) is called a complex fraction. In other words, a complex fraction is a fractional expression divided by another fractional expression.We want to simplify complex fractions to regular fractions.The “easy” complex fractions are just regular divisions of of a fraction by another fraction. In this case just flip the denominator then simplify the multiplication,
![Page 7: 16 the multiplier method for simplifying complex fractions](https://reader035.vdocuments.mx/reader035/viewer/2022062515/55cfa04bbb61eb503f8b4692/html5/thumbnails/7.jpg)
Complex FractionsA fraction with its numerator or the denominator containing fraction(s) is called a complex fraction. In other words, a complex fraction is a fractional expression divided by another fractional expression.We want to simplify complex fractions to regular fractions.The “easy” complex fractions are just regular divisions of of a fraction by another fraction. In this case just flip the denominator then simplify the multiplication, i.e.
ABCD
![Page 8: 16 the multiplier method for simplifying complex fractions](https://reader035.vdocuments.mx/reader035/viewer/2022062515/55cfa04bbb61eb503f8b4692/html5/thumbnails/8.jpg)
Complex FractionsA fraction with its numerator or the denominator containing fraction(s) is called a complex fraction. In other words, a complex fraction is a fractional expression divided by another fractional expression.We want to simplify complex fractions to regular fractions.The “easy” complex fractions are just regular divisions of of a fraction by another fraction. In this case just flip the denominator then simplify the multiplication, i.e.
ABCD
AB C
D*
flip
![Page 9: 16 the multiplier method for simplifying complex fractions](https://reader035.vdocuments.mx/reader035/viewer/2022062515/55cfa04bbb61eb503f8b4692/html5/thumbnails/9.jpg)
Complex FractionsA fraction with its numerator or the denominator containing fraction(s) is called a complex fraction. In other words, a complex fraction is a fractional expression divided by another fractional expression.We want to simplify complex fractions to regular fractions.The “easy” complex fractions are just regular divisions of of a fraction by another fraction. In this case just flip the denominator then simplify the multiplication, i.e.
ABCD
AB C
D*
flip
Example A. Simplify
4x2y9xy2
6
![Page 10: 16 the multiplier method for simplifying complex fractions](https://reader035.vdocuments.mx/reader035/viewer/2022062515/55cfa04bbb61eb503f8b4692/html5/thumbnails/10.jpg)
Complex FractionsA fraction with its numerator or the denominator containing fraction(s) is called a complex fraction. In other words, a complex fraction is a fractional expression divided by another fractional expression.We want to simplify complex fractions to regular fractions.The “easy” complex fractions are just regular divisions of of a fraction by another fraction. In this case just flip the denominator then simplify the multiplication, i.e.
ABCD
AB C
D*
flip
Example A. Simplify
4x2y9xy2
6
=
flip
4x2y9 xy2
6
![Page 11: 16 the multiplier method for simplifying complex fractions](https://reader035.vdocuments.mx/reader035/viewer/2022062515/55cfa04bbb61eb503f8b4692/html5/thumbnails/11.jpg)
Complex FractionsA fraction with its numerator or the denominator containing fraction(s) is called a complex fraction. In other words, a complex fraction is a fractional expression divided by another fractional expression.We want to simplify complex fractions to regular fractions.The “easy” complex fractions are just regular divisions of of a fraction by another fraction. In this case just flip the denominator then simplify the multiplication, i.e.
ABCD
AB C
D*
flip
Example A. Simplify
4x2y9xy2
6
=
flip
4x2y9 xy2
63
2
![Page 12: 16 the multiplier method for simplifying complex fractions](https://reader035.vdocuments.mx/reader035/viewer/2022062515/55cfa04bbb61eb503f8b4692/html5/thumbnails/12.jpg)
Complex FractionsA fraction with its numerator or the denominator containing fraction(s) is called a complex fraction. In other words, a complex fraction is a fractional expression divided by another fractional expression.We want to simplify complex fractions to regular fractions.The “easy” complex fractions are just regular divisions of of a fraction by another fraction. In this case just flip the denominator then simplify the multiplication, i.e.
ABCD
AB C
D*
flip
Example A. Simplify
4x2y9xy2
6
=
flip
4x2y9 xy2
63
2x
![Page 13: 16 the multiplier method for simplifying complex fractions](https://reader035.vdocuments.mx/reader035/viewer/2022062515/55cfa04bbb61eb503f8b4692/html5/thumbnails/13.jpg)
Complex FractionsA fraction with its numerator or the denominator containing fraction(s) is called a complex fraction. In other words, a complex fraction is a fractional expression divided by another fractional expression.We want to simplify complex fractions to regular fractions.The “easy” complex fractions are just regular divisions of of a fraction by another fraction. In this case just flip the denominator then simplify the multiplication, i.e.
ABCD
AB C
D*
flip
Example A. Simplify
4x2y9xy2
6
=
flip
4x2y9 xy2
63
2x
y
![Page 14: 16 the multiplier method for simplifying complex fractions](https://reader035.vdocuments.mx/reader035/viewer/2022062515/55cfa04bbb61eb503f8b4692/html5/thumbnails/14.jpg)
Complex FractionsA fraction with its numerator or the denominator containing fraction(s) is called a complex fraction. In other words, a complex fraction is a fractional expression divided by another fractional expression.We want to simplify complex fractions to regular fractions.The “easy” complex fractions are just regular divisions of of a fraction by another fraction. In this case just flip the denominator then simplify the multiplication, i.e.
ABCD
AB C
D*
flip
Example A. Simplify
4x2y9xy2
6
=
flip
4x2y9 xy2
6 =3
2x
y
8x3y
![Page 15: 16 the multiplier method for simplifying complex fractions](https://reader035.vdocuments.mx/reader035/viewer/2022062515/55cfa04bbb61eb503f8b4692/html5/thumbnails/15.jpg)
Complex FractionsWe give two methods for simplifying general complex fractions.
![Page 16: 16 the multiplier method for simplifying complex fractions](https://reader035.vdocuments.mx/reader035/viewer/2022062515/55cfa04bbb61eb503f8b4692/html5/thumbnails/16.jpg)
Complex FractionsWe give two methods for simplifying general complex fractions. The first method is to reduce the problem to an “easy” problem.
![Page 17: 16 the multiplier method for simplifying complex fractions](https://reader035.vdocuments.mx/reader035/viewer/2022062515/55cfa04bbb61eb503f8b4692/html5/thumbnails/17.jpg)
Complex FractionsWe give two methods for simplifying general complex fractions. The first method is to reduce the problem to an “easy” problem. We do this by combining the numerator into one fraction and the denominator into one fraction.
![Page 18: 16 the multiplier method for simplifying complex fractions](https://reader035.vdocuments.mx/reader035/viewer/2022062515/55cfa04bbb61eb503f8b4692/html5/thumbnails/18.jpg)
Complex FractionsWe give two methods for simplifying general complex fractions. The first method is to reduce the problem to an “easy” problem. We do this by combining the numerator into one fraction and the denominator into one fraction. We can use cross multiplication for combining two fractions.
![Page 19: 16 the multiplier method for simplifying complex fractions](https://reader035.vdocuments.mx/reader035/viewer/2022062515/55cfa04bbb61eb503f8b4692/html5/thumbnails/19.jpg)
Example B. Simplify
Complex FractionsWe give two methods for simplifying general complex fractions. The first method is to reduce the problem to an “easy” problem. We do this by combining the numerator into one fraction and the denominator into one fraction. We can use cross multiplication for combining two fractions. x
x + 1 + 1
1 – xx – 1
![Page 20: 16 the multiplier method for simplifying complex fractions](https://reader035.vdocuments.mx/reader035/viewer/2022062515/55cfa04bbb61eb503f8b4692/html5/thumbnails/20.jpg)
Example B. Simplify
Complex FractionsWe give two methods for simplifying general complex fractions. The first method is to reduce the problem to an “easy” problem. We do this by combining the numerator into one fraction and the denominator into one fraction. We can use cross multiplication for combining two fractions. x
x + 1 + 1
1 – xx – 1 x
x + 1 + 1
1 – xx – 1
![Page 21: 16 the multiplier method for simplifying complex fractions](https://reader035.vdocuments.mx/reader035/viewer/2022062515/55cfa04bbb61eb503f8b4692/html5/thumbnails/21.jpg)
Example B. Simplify
Complex FractionsWe give two methods for simplifying general complex fractions. The first method is to reduce the problem to an “easy” problem. We do this by combining the numerator into one fraction and the denominator into one fraction. We can use cross multiplication for combining two fractions. x
x + 1 + 1
1 – xx – 1 x
x + 1 + 1
1 – xx – 1
=
xx + 1 +
– xx – 1
11
11
![Page 22: 16 the multiplier method for simplifying complex fractions](https://reader035.vdocuments.mx/reader035/viewer/2022062515/55cfa04bbb61eb503f8b4692/html5/thumbnails/22.jpg)
Example B. Simplify
Complex FractionsWe give two methods for simplifying general complex fractions. The first method is to reduce the problem to an “easy” problem. We do this by combining the numerator into one fraction and the denominator into one fraction. We can use cross multiplication for combining two fractions. x
x + 1 + 1
1 – xx – 1 x
x + 1 + 1
1 – xx – 1
=
xx + 1 +
– xx – 1
11
11
=
x + (x + 1)x + 1
![Page 23: 16 the multiplier method for simplifying complex fractions](https://reader035.vdocuments.mx/reader035/viewer/2022062515/55cfa04bbb61eb503f8b4692/html5/thumbnails/23.jpg)
Example B. Simplify
Complex FractionsWe give two methods for simplifying general complex fractions. The first method is to reduce the problem to an “easy” problem. We do this by combining the numerator into one fraction and the denominator into one fraction. We can use cross multiplication for combining two fractions. x
x + 1 + 1
1 – xx – 1 x
x + 1 + 1
1 – xx – 1
=
xx + 1 +
– xx – 1
11
11
=
x + (x + 1)x + 1(x – 1) – x
x – 1
![Page 24: 16 the multiplier method for simplifying complex fractions](https://reader035.vdocuments.mx/reader035/viewer/2022062515/55cfa04bbb61eb503f8b4692/html5/thumbnails/24.jpg)
Example B. Simplify
Complex FractionsWe give two methods for simplifying general complex fractions. The first method is to reduce the problem to an “easy” problem. We do this by combining the numerator into one fraction and the denominator into one fraction. We can use cross multiplication for combining two fractions. x
x + 1 + 1
1 – xx – 1 x
x + 1 + 1
1 – xx – 1
=
xx + 1 +
– xx – 1
11
11
=
x + (x + 1)x + 1(x – 1) – x
x – 1
=
2x + 1x + 1
–1x – 1
![Page 25: 16 the multiplier method for simplifying complex fractions](https://reader035.vdocuments.mx/reader035/viewer/2022062515/55cfa04bbb61eb503f8b4692/html5/thumbnails/25.jpg)
Complex Fractions
xx + 1 + 1
1 – xx – 1
=
2x + 1x + 1
–1x – 1
Therefore,
![Page 26: 16 the multiplier method for simplifying complex fractions](https://reader035.vdocuments.mx/reader035/viewer/2022062515/55cfa04bbb61eb503f8b4692/html5/thumbnails/26.jpg)
Complex Fractions
xx + 1 + 1
1 – xx – 1
=
2x + 1x + 1
–1x – 1
Therefore,
= (2x + 1)(x + 1)
(x – 1) (–1)
![Page 27: 16 the multiplier method for simplifying complex fractions](https://reader035.vdocuments.mx/reader035/viewer/2022062515/55cfa04bbb61eb503f8b4692/html5/thumbnails/27.jpg)
Complex Fractions
xx + 1 + 1
1 – xx – 1
=
2x + 1x + 1
–1x – 1
Therefore,
= (2x + 1)(x + 1)
(x – 1) = – (2x + 1)(x + 1)
(x – 1) (–1)
![Page 28: 16 the multiplier method for simplifying complex fractions](https://reader035.vdocuments.mx/reader035/viewer/2022062515/55cfa04bbb61eb503f8b4692/html5/thumbnails/28.jpg)
Complex Fractions
xx + 1 + 1
1 – xx – 1
=
Therefore,
The second method is to multiply the LCD of all the terms to the numerator and the denominator of the complex fraction.
2x + 1x + 1
–1x – 1
= (2x + 1)(x + 1)
(x – 1) = – (2x + 1)(x + 1)
(x – 1) (–1)
![Page 29: 16 the multiplier method for simplifying complex fractions](https://reader035.vdocuments.mx/reader035/viewer/2022062515/55cfa04bbb61eb503f8b4692/html5/thumbnails/29.jpg)
Complex Fractions
xx + 1 + 1
1 – xx – 1
=
Therefore,
The second method is to multiply the LCD of all the terms to the numerator and the denominator of the complex fraction.
Example C. Simplify
32 + 1
1 –
– 56
23
34+
2x + 1x + 1
–1x – 1
= (2x + 1)(x + 1)
(x – 1) = – (2x + 1)(x + 1)
(x – 1) (–1)
![Page 30: 16 the multiplier method for simplifying complex fractions](https://reader035.vdocuments.mx/reader035/viewer/2022062515/55cfa04bbb61eb503f8b4692/html5/thumbnails/30.jpg)
Complex Fractions
xx + 1 + 1
1 – xx – 1
=
Therefore,
The second method is to multiply the LCD of all the terms to the numerator and the denominator of the complex fraction.
Example C. Simplify
32 + 1
1 –
– 56
23
34+
The LCD of 23
32
56
34, , , is 12.
2x + 1x + 1
–1x – 1
= (2x + 1)(x + 1)
(x – 1) = – (2x + 1)(x + 1)
(x – 1) (–1)
![Page 31: 16 the multiplier method for simplifying complex fractions](https://reader035.vdocuments.mx/reader035/viewer/2022062515/55cfa04bbb61eb503f8b4692/html5/thumbnails/31.jpg)
Complex Fractions
xx + 1 + 1
1 – xx – 1
=
Therefore,
The second method is to multiply the LCD of all the terms to the numerator and the denominator of the complex fraction.
Example C. Simplify
32 + 1
1 –
– 56
23
34+
The LCD of 23
32
56
34, , , is 12.
Multiply 12 to the top and bottom of the complex fraction.32 + 1
1 –
– 56
23
34+
2x + 1x + 1
–1x – 1
= (2x + 1)(x + 1) (–1)
(x – 1) = – (2x + 1)(x + 1)
(x – 1)
![Page 32: 16 the multiplier method for simplifying complex fractions](https://reader035.vdocuments.mx/reader035/viewer/2022062515/55cfa04bbb61eb503f8b4692/html5/thumbnails/32.jpg)
Complex Fractions
xx + 1 + 1
1 – xx – 1
=
Therefore,
The second method is to multiply the LCD of all the terms to the numerator and the denominator of the complex fraction.
Example C. Simplify
32 + 1
1 –
– 56
23
34+
The LCD of 23
32
56
34, , , is 12.
Multiply 12 to the top and bottom of the complex fraction.32 + 1
1 –
– 56
23
34+ (
( ))
12
12
2x + 1x + 1
–1x – 1
= (2x + 1)(x + 1) (–1)
(x – 1) = – (2x + 1)(x + 1)
(x – 1)
![Page 33: 16 the multiplier method for simplifying complex fractions](https://reader035.vdocuments.mx/reader035/viewer/2022062515/55cfa04bbb61eb503f8b4692/html5/thumbnails/33.jpg)
Complex Fractions
xx + 1 + 1
1 – xx – 1
=
Therefore,
The second method is to multiply the LCD of all the terms to the numerator and the denominator of the complex fraction.
Example C. Simplify
32 + 1
1 –
– 56
23
34+
The LCD of 23
32
56
34, , , is 12.
Multiply 12 to the top and bottom of the complex fraction.32 + 1
1 –
– 56
23
34+ (
( ))
12
12
2x + 1x + 1
–1x – 1
= (2x + 1)(x + 1)
(x – 1) = – (2x + 1)(x + 1)
(x – 1)
This is OK since is 1.12121
(–1)
![Page 34: 16 the multiplier method for simplifying complex fractions](https://reader035.vdocuments.mx/reader035/viewer/2022062515/55cfa04bbb61eb503f8b4692/html5/thumbnails/34.jpg)
Complex Fractions
xx + 1 + 1
1 – xx – 1
=
Therefore,
The second method is to multiply the LCD of all the terms to the numerator and the denominator of the complex fraction.
Example C. Simplify
32 + 1
1 –
– 56
23
34+
The LCD of 23
32
56
34, , , is 12.
Multiply 12 to the top and bottom of the complex fraction.32 + 1
1 –
– 56
23
34+ (
( ))
12
12
6
2x + 1x + 1
–1x – 1
= (2x + 1)(x + 1)
(x – 1) = – (2x + 1)(x + 1)
(x – 1)
Distribute the multiplication.
(–1)
![Page 35: 16 the multiplier method for simplifying complex fractions](https://reader035.vdocuments.mx/reader035/viewer/2022062515/55cfa04bbb61eb503f8b4692/html5/thumbnails/35.jpg)
Complex Fractions
xx + 1 + 1
1 – xx – 1
=
Therefore,
The second method is to multiply the LCD of all the terms to the numerator and the denominator of the complex fraction.
Example C. Simplify
32 + 1
1 –
– 56
23
34+
The LCD of 23
32
56
34, , , is 12.
Multiply 12 to the top and bottom of the complex fraction.32 + 1
1 –
– 56
23
34+ (
( ))
12
12
6 12
2x + 1x + 1
–1x – 1
= (2x + 1)(x + 1)
(x – 1) = – (2x + 1)(x + 1)
(x – 1)
Distribute the multiplication.
(–1)
![Page 36: 16 the multiplier method for simplifying complex fractions](https://reader035.vdocuments.mx/reader035/viewer/2022062515/55cfa04bbb61eb503f8b4692/html5/thumbnails/36.jpg)
Complex Fractions
xx + 1 + 1
1 – xx – 1
=
Therefore,
The second method is to multiply the LCD of all the terms to the numerator and the denominator of the complex fraction.
Example C. Simplify
32 + 1
1 –
– 56
23
34+
The LCD of 23
32
56
34, , , is 12.
Multiply 12 to the top and bottom of the complex fraction.32 + 1
1 –
– 56
23
34+ (
( ))
12
12
6 12 2
2x + 1x + 1
–1x – 1
= (2x + 1)(x + 1)
(x – 1) = – (2x + 1)(x + 1)
(x – 1)
Distribute the multiplication.
(–1)
![Page 37: 16 the multiplier method for simplifying complex fractions](https://reader035.vdocuments.mx/reader035/viewer/2022062515/55cfa04bbb61eb503f8b4692/html5/thumbnails/37.jpg)
Complex Fractions
xx + 1 + 1
1 – xx – 1
=
Therefore,
The second method is to multiply the LCD of all the terms to the numerator and the denominator of the complex fraction.
Example C. Simplify
32 + 1
1 –
– 56
23
34+
The LCD of 23
32
56
34, , , is 12.
Multiply 12 to the top and bottom of the complex fraction.32 + 1
1 –
– 56
23
34+ (
( ))
12
12
6 12 2
12 4 3
2x + 1x + 1
–1x – 1
= (2x + 1)(x + 1)
(x – 1) = – (2x + 1)(x + 1)
(x – 1)
Distribute the multiplication.
(–1)
![Page 38: 16 the multiplier method for simplifying complex fractions](https://reader035.vdocuments.mx/reader035/viewer/2022062515/55cfa04bbb61eb503f8b4692/html5/thumbnails/38.jpg)
Complex Fractions
xx + 1 + 1
1 – xx – 1
=
Therefore,
The second method is to multiply the LCD of all the terms to the numerator and the denominator of the complex fraction.
Example C. Simplify
32 + 1
1 –
– 56
23
34+
The LCD of 23
32
56
34, , , is 12.
Multiply 12 to the top and bottom of the complex fraction.32 + 1
1 –
– 56
23
34+ (
( ))
12
12=
6 12 2
12 4 318 + 12 – 1012 – 8 + 9
2x + 1x + 1
–1x – 1
= (2x + 1)(x + 1)
(x – 1) = – (2x + 1)(x + 1)
(x – 1) (–1)
![Page 39: 16 the multiplier method for simplifying complex fractions](https://reader035.vdocuments.mx/reader035/viewer/2022062515/55cfa04bbb61eb503f8b4692/html5/thumbnails/39.jpg)
Complex Fractions
xx + 1 + 1
1 – xx – 1
=
Therefore,
The second method is to multiply the LCD of all the terms to the numerator and the denominator of the complex fraction.
Example C. Simplify
32 + 1
1 –
– 56
23
34+
The LCD of 23
32
56
34, , , is 12.
Multiply 12 to the top and bottom of the complex fraction.32 + 1
1 –
– 56
23
34+ (
( ))
12
12=
6 12 2
12 4 318 + 12 – 1012 – 8 + 9 = 20
13
2x + 1x + 1
–1x – 1
= (2x + 1)(x + 1)
(x – 1) = – (2x + 1)(x + 1)
(x – 1) (–1)
![Page 40: 16 the multiplier method for simplifying complex fractions](https://reader035.vdocuments.mx/reader035/viewer/2022062515/55cfa04bbb61eb503f8b4692/html5/thumbnails/40.jpg)
Complex Fractionsx2
+ 1
– 1 Example D. Simplify x
y
y2
![Page 41: 16 the multiplier method for simplifying complex fractions](https://reader035.vdocuments.mx/reader035/viewer/2022062515/55cfa04bbb61eb503f8b4692/html5/thumbnails/41.jpg)
Complex Fractionsx2
+ 1
– 1 Example D. Simplify
The LCD of
xy
is y2.
y2
x2
xy y2 ,
![Page 42: 16 the multiplier method for simplifying complex fractions](https://reader035.vdocuments.mx/reader035/viewer/2022062515/55cfa04bbb61eb503f8b4692/html5/thumbnails/42.jpg)
Complex Fractionsx2
+ 1
– 1 Example D. Simplify
The LCD of
xy
is y2.
Multiply the LCD to top and bottom of the complex fraction.
y2
x2
xy y2 ,
x2
+ 1
– 1
xy
y2
![Page 43: 16 the multiplier method for simplifying complex fractions](https://reader035.vdocuments.mx/reader035/viewer/2022062515/55cfa04bbb61eb503f8b4692/html5/thumbnails/43.jpg)
Complex Fractionsx2
+ 1
– 1 Example D. Simplify
The LCD of
xy
is y2.
Multiply the LCD to top and bottom of the complex fraction.
y2
x2
xy y2 ,
x2
+ 1
– 1
xy
y2
((
)) y2
y2
![Page 44: 16 the multiplier method for simplifying complex fractions](https://reader035.vdocuments.mx/reader035/viewer/2022062515/55cfa04bbb61eb503f8b4692/html5/thumbnails/44.jpg)
Complex Fractionsx2
+ 1
– 1 Example D. Simplify
The LCD of
xy
is y2.
Multiply the LCD to top and bottom of the complex fraction.
y2
x2
xy y2 ,
x2
+ 1
– 1
xy
y2
((
)) y2
y2
1
![Page 45: 16 the multiplier method for simplifying complex fractions](https://reader035.vdocuments.mx/reader035/viewer/2022062515/55cfa04bbb61eb503f8b4692/html5/thumbnails/45.jpg)
Complex Fractionsx2
+ 1
– 1 Example D. Simplify
The LCD of
xy
is y2.
Multiply the LCD to top and bottom of the complex fraction.
y2
x2
xy y2 ,
x2
+ 1
– 1
xy
y2
((
)) y2
y2
y21
![Page 46: 16 the multiplier method for simplifying complex fractions](https://reader035.vdocuments.mx/reader035/viewer/2022062515/55cfa04bbb61eb503f8b4692/html5/thumbnails/46.jpg)
Complex Fractionsx2
+ 1
– 1 Example D. Simplify
The LCD of
xy
is y2.
Multiply the LCD to top and bottom of the complex fraction.
y2
x2
xy y2 ,
x2
+ 1
– 1
xy
y2
((
)) y2
y2
y2
y2y
1
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Complex Fractionsx2
+ 1
– 1 Example D. Simplify
The LCD of
xy
is y2.
Multiply the LCD to top and bottom of the complex fraction.
y2
x2
xy y2 ,
x2
+ 1
– 1
xy
y2
((
)) y2
y2
=
y2
y2y
1
x2 – y2
xy + y2
![Page 48: 16 the multiplier method for simplifying complex fractions](https://reader035.vdocuments.mx/reader035/viewer/2022062515/55cfa04bbb61eb503f8b4692/html5/thumbnails/48.jpg)
Complex Fractionsx2
+ 1
– 1 Example D. Simplify
The LCD of
xy
is y2.
Multiply the LCD to top and bottom of the complex fraction.
y2
x2
xy y2 ,
x2
+ 1
– 1
xy
y2
((
)) y2
y2
=
y2
y2y
1
x2 – y2
xy + y2
= (x – y)(x + y)y(x + y)
To simplify this, put it in the factored form .
![Page 49: 16 the multiplier method for simplifying complex fractions](https://reader035.vdocuments.mx/reader035/viewer/2022062515/55cfa04bbb61eb503f8b4692/html5/thumbnails/49.jpg)
Complex Fractionsx2
+ 1
– 1 Example D. Simplify
The LCD of
xy
is y2.
Multiply the LCD to top and bottom of the complex fraction.
y2
x2
xy y2 ,
x2
+ 1
– 1
xy
y2
((
)) y2
y2
=
y2
y2y
1
x2 – y2
xy + y2 To simplify this, put it in the factored form .
= (x – y)(x + y)y(x + y)
![Page 50: 16 the multiplier method for simplifying complex fractions](https://reader035.vdocuments.mx/reader035/viewer/2022062515/55cfa04bbb61eb503f8b4692/html5/thumbnails/50.jpg)
Complex Fractionsx2
+ 1
– 1 Example D. Simplify
The LCD of
xy
is y2.
Multiply the LCD to top and bottom of the complex fraction.
y2
x2
xy y2 ,
x2
+ 1
– 1
xy
y2
((
)) y2
y2
=
y2
y2y
1
x2 – y2
xy + y2 To simplify this, put it in the factored form .
= (x – y)(x + y)y(x + y)
= x – y y
![Page 51: 16 the multiplier method for simplifying complex fractions](https://reader035.vdocuments.mx/reader035/viewer/2022062515/55cfa04bbb61eb503f8b4692/html5/thumbnails/51.jpg)
Complex Fractionsx
x – 2
–
+
3x + 2
Example E. Simplify
3x + 2
xx – 2
![Page 52: 16 the multiplier method for simplifying complex fractions](https://reader035.vdocuments.mx/reader035/viewer/2022062515/55cfa04bbb61eb503f8b4692/html5/thumbnails/52.jpg)
Complex Fractionsx
x – 2
–
+
3x + 2
Example E. Simplify
The LCD of
3x + 2
xx – 2
xx – 2
xx – 2
3x + 2
3x + 2 , , , is (x – 2)(x + 2).
![Page 53: 16 the multiplier method for simplifying complex fractions](https://reader035.vdocuments.mx/reader035/viewer/2022062515/55cfa04bbb61eb503f8b4692/html5/thumbnails/53.jpg)
Complex Fractionsx
x – 2
–
+
3x + 2
Example E. Simplify
The LCD of
3x + 2
xx – 2
xx – 2
xx – 2
3x + 2
3x + 2 , , , is (x – 2)(x + 2).
Multiply the LCD to top and bottom of the complex fraction.
xx – 2
–
+
3x + 2
3x + 2
xx – 2
![Page 54: 16 the multiplier method for simplifying complex fractions](https://reader035.vdocuments.mx/reader035/viewer/2022062515/55cfa04bbb61eb503f8b4692/html5/thumbnails/54.jpg)
Complex Fractionsx
x – 2
–
+
3x + 2
Example E. Simplify
The LCD of
3x + 2
xx – 2
xx – 2
xx – 2
3x + 2
3x + 2 , , , is (x – 2)(x + 2).
Multiply the LCD to top and bottom of the complex fraction.
xx – 2
–
+
3x + 2
3x + 2
xx – 2 (
( ))
(x – 2)(x + 2)
(x – 2)(x + 2)
![Page 55: 16 the multiplier method for simplifying complex fractions](https://reader035.vdocuments.mx/reader035/viewer/2022062515/55cfa04bbb61eb503f8b4692/html5/thumbnails/55.jpg)
Complex Fractionsx
x – 2
–
+
3x + 2
Example E. Simplify
The LCD of
3x + 2
xx – 2
xx – 2
xx – 2
3x + 2
3x + 2 , , , is (x – 2)(x + 2).
Multiply the LCD to top and bottom of the complex fraction.
xx – 2
–
+
3x + 2
3x + 2
xx – 2 (
( ))
(x – 2)(x + 2)
(x – 2)(x + 2)
(x + 2)
![Page 56: 16 the multiplier method for simplifying complex fractions](https://reader035.vdocuments.mx/reader035/viewer/2022062515/55cfa04bbb61eb503f8b4692/html5/thumbnails/56.jpg)
Complex Fractionsx
x – 2
–
+
3x + 2
Example E. Simplify
The LCD of
3x + 2
xx – 2
xx – 2
xx – 2
3x + 2
3x + 2 , , , is (x – 2)(x + 2).
Multiply the LCD to top and bottom of the complex fraction.
xx – 2
–
+
3x + 2
3x + 2
xx – 2 (
( ))
(x – 2)(x + 2)
(x – 2)(x + 2)
(x + 2) (x – 2)
![Page 57: 16 the multiplier method for simplifying complex fractions](https://reader035.vdocuments.mx/reader035/viewer/2022062515/55cfa04bbb61eb503f8b4692/html5/thumbnails/57.jpg)
Complex Fractionsx
x – 2
–
+
3x + 2
Example E. Simplify
The LCD of
3x + 2
xx – 2
xx – 2
xx – 2
3x + 2
3x + 2 , , , is (x – 2)(x + 2).
Multiply the LCD to top and bottom of the complex fraction.
xx – 2
–
+
3x + 2
3x + 2
xx – 2 (
( ))
(x – 2)(x + 2)
(x – 2)(x + 2)
=
(x + 2)
(x + 2)
(x – 2)
(x – 2)
x(x + 2) + 3(x – 2)x(x + 2) – 3(x – 2) Expand and put the fraction
in the factored form.
![Page 58: 16 the multiplier method for simplifying complex fractions](https://reader035.vdocuments.mx/reader035/viewer/2022062515/55cfa04bbb61eb503f8b4692/html5/thumbnails/58.jpg)
Complex Fractionsx
x – 2
–
+
3x + 2
Example E. Simplify
The LCD of
3x + 2
xx – 2
xx – 2
xx – 2
3x + 2
3x + 2 , , , is (x – 2)(x + 2).
Multiply the LCD to top and bottom of the complex fraction.
xx – 2
–
+
3x + 2
3x + 2
xx – 2 (
( ))
(x – 2)(x + 2)
(x – 2)(x + 2)
=
(x + 2)
(x + 2)
(x – 2)
(x – 2)
x(x + 2) + 3(x – 2)x(x + 2) – 3(x – 2) Expand and put the fraction
in the factored form. = x2 + 2x + 3x – 6
x2 + 2x – 3x + 6
![Page 59: 16 the multiplier method for simplifying complex fractions](https://reader035.vdocuments.mx/reader035/viewer/2022062515/55cfa04bbb61eb503f8b4692/html5/thumbnails/59.jpg)
Complex Fractionsx
x – 2
–
+
3x + 2
Example E. Simplify
The LCD of
3x + 2
xx – 2
xx – 2
xx – 2
3x + 2
3x + 2 , , , is (x – 2)(x + 2).
Multiply the LCD to top and bottom of the complex fraction.
xx – 2
–
+
3x + 2
3x + 2
xx – 2 (
( ))
(x – 2)(x + 2)
(x – 2)(x + 2)
=
(x + 2)
(x + 2)
(x – 2)
(x – 2)
x(x + 2) + 3(x – 2)x(x + 2) – 3(x – 2) Expand and put the fraction
in the factored form. = x2 + 2x + 3x – 6
x2 + 2x – 3x + 6
= x2 + 5x – 6x2 – x + 6
![Page 60: 16 the multiplier method for simplifying complex fractions](https://reader035.vdocuments.mx/reader035/viewer/2022062515/55cfa04bbb61eb503f8b4692/html5/thumbnails/60.jpg)
Complex Fractionsx
x – 2
–
+
3x + 2
Example E. Simplify
The LCD of
3x + 2
xx – 2
xx – 2
xx – 2
3x + 2
3x + 2 , , , is (x – 2)(x + 2).
Multiply the LCD to top and bottom of the complex fraction.
xx – 2
–
+
3x + 2
3x + 2
xx – 2 (
( ))
(x – 2)(x + 2)
(x – 2)(x + 2)
=
(x + 2)
(x + 2)
(x – 2)
(x – 2)
x(x + 2) + 3(x – 2)x(x + 2) – 3(x – 2) Expand and put the fraction
in the factored form. = x2 + 2x + 3x – 6
x2 + 2x – 3x + 6
= x2 + 5x – 6x2 – x + 6
This is the simplified.= (x + 6)(x – 1)x2 – x + 6
![Page 61: 16 the multiplier method for simplifying complex fractions](https://reader035.vdocuments.mx/reader035/viewer/2022062515/55cfa04bbb61eb503f8b4692/html5/thumbnails/61.jpg)
Complex Fractions2
x – 1
–
+
3x + 2
Example F. Simplify
3x + 2
1x – 2
![Page 62: 16 the multiplier method for simplifying complex fractions](https://reader035.vdocuments.mx/reader035/viewer/2022062515/55cfa04bbb61eb503f8b4692/html5/thumbnails/62.jpg)
Complex Fractions2
x – 1
–
+
3x + 2
Example F. Simplify
3x + 2
1x – 2
Use the crossing method.
![Page 63: 16 the multiplier method for simplifying complex fractions](https://reader035.vdocuments.mx/reader035/viewer/2022062515/55cfa04bbb61eb503f8b4692/html5/thumbnails/63.jpg)
Complex Fractions2
x – 1
–
+
3x + 2
Example F. Simplify
3x + 2
1x – 2
Use the crossing method.2
x – 1
–
+
3x + 2
3x + 2
1x – 2
![Page 64: 16 the multiplier method for simplifying complex fractions](https://reader035.vdocuments.mx/reader035/viewer/2022062515/55cfa04bbb61eb503f8b4692/html5/thumbnails/64.jpg)
Complex Fractions2
x – 1
–
+
3x + 2
Example F. Simplify
3x + 2
1x – 2
Use the crossing method.2
x – 1
–
+
3x + 2
3x + 2
1x – 2
=
2(x + 2) + 3(x – 1)(x – 1)(x + 2)
2(x + 3) – 3(x – 2)(x – 2)(x + 2)
![Page 65: 16 the multiplier method for simplifying complex fractions](https://reader035.vdocuments.mx/reader035/viewer/2022062515/55cfa04bbb61eb503f8b4692/html5/thumbnails/65.jpg)
Complex Fractions2
x – 1
–
+
3x + 2
Example F. Simplify
3x + 2
1x – 2
Use the crossing method.2
x – 1
–
+
3x + 2
3x + 2
1x – 2
=
2(x + 2) + 3(x – 1)(x – 1)(x + 2)
2(x + 3) – 3(x – 2)(x – 2)(x + 2)
=
5x +1(x – 1)(x + 2) – x + 12
(x – 2)(x + 2)
![Page 66: 16 the multiplier method for simplifying complex fractions](https://reader035.vdocuments.mx/reader035/viewer/2022062515/55cfa04bbb61eb503f8b4692/html5/thumbnails/66.jpg)
Complex Fractions2
x – 1
–
+
3x + 2
Example F. Simplify
3x + 2
1x – 2
Use the crossing method.2
x – 1
–
+
3x + 2
3x + 2
1x – 2
=
2(x + 2) + 3(x – 1)(x – 1)(x + 2)
2(x + 3) – 3(x – 2)(x – 2)(x + 2)
flip the bottom fraction
=
5x +1(x – 1)(x + 2) – x + 12
(x – 2)(x + 2)
![Page 67: 16 the multiplier method for simplifying complex fractions](https://reader035.vdocuments.mx/reader035/viewer/2022062515/55cfa04bbb61eb503f8b4692/html5/thumbnails/67.jpg)
Complex Fractions2
x – 1
–
+
3x + 2
Example F. Simplify
3x + 2
1x – 2
Use the crossing method.2
x – 1
–
+
3x + 2
3x + 2
1x – 2
=
2(x + 2) + 3(x – 1)(x – 1)(x + 2)
2(x + 3) – 3(x – 2)(x – 2)(x + 2)
flip the bottom fraction
=
5x +1(x – 1)(x + 2) – x + 12
(x – 2)(x + 2)
=(5x +1)
(x – 1)(x + 2) (– x + 12)(x – 2)(x + 2)
![Page 68: 16 the multiplier method for simplifying complex fractions](https://reader035.vdocuments.mx/reader035/viewer/2022062515/55cfa04bbb61eb503f8b4692/html5/thumbnails/68.jpg)
Complex Fractions2
x – 1
–
+
3x + 2
Example F. Simplify
3x + 2
1x – 2
Use the crossing method.2
x – 1
–
+
3x + 2
3x + 2
1x – 2
=
2(x + 2) + 3(x – 1)(x – 1)(x + 2)
2(x + 3) – 3(x – 2)(x – 2)(x + 2)
flip the bottom fraction
=
5x +1(x – 1)(x + 2) – x + 12
(x – 2)(x + 2)
=(5x +1)
(x – 1)(x + 2) (– x + 12)(x – 2)(x + 2)
=(5x + 1)(x – 2)(x – 1)(–x + 12)
![Page 69: 16 the multiplier method for simplifying complex fractions](https://reader035.vdocuments.mx/reader035/viewer/2022062515/55cfa04bbb61eb503f8b4692/html5/thumbnails/69.jpg)
Complex FractionsEx. A. Simplify.
1.
2x2y54y2 2.
34x2
3x2 3. 4x2
2x3 4.
12x2
5y4xy15
3
+ 1
–
13
45.
2 3
5
–
–
23
66.
4 314
4
+
–
16
57.
11 15712
1
+ 1
– 2
2y
x8.1
+ 2
1 –
1x2
xy9.1
+
–
1x
y10.1x
1y
2
–
–
4x2
y11.2x
4y2
2
–
–
4x2
y12.2x
4y2
2x + 1 + 1
1 – 1x – 1
13.
![Page 70: 16 the multiplier method for simplifying complex fractions](https://reader035.vdocuments.mx/reader035/viewer/2022062515/55cfa04bbb61eb503f8b4692/html5/thumbnails/70.jpg)
Complex Fractions1
2x + 1 – 2
3 – 1x + 2
14.
2x – 3 – 1
2 – 12x + 1
15.
2x + 3 –
+ 1x + 3
16.
3x + 2
3x + 2
–2 2x + 1 –
+ 3x + 4
17.
1x + 4
22x + 1
2 x + 2 –
+ 2x + 5
18.
13x – 1
3x + 2
4 2x + 3 –
+ 3x + 4
19.
33x – 2
53x – 2
–5 2x + 5 –
+ 3–x + 4
20.
22x – 3
62x – 3
23 + 2
2 –
– 16
23
12+
21.
12 – + 56
23
14–
22.34
32 +
![Page 71: 16 the multiplier method for simplifying complex fractions](https://reader035.vdocuments.mx/reader035/viewer/2022062515/55cfa04bbb61eb503f8b4692/html5/thumbnails/71.jpg)
Complex Fractions
23.
2x – 1
–
+
3x + 3
xx + 3
xx – 1
24.
3x + 2
–
+
3x + 2
xx – 2
xx – 2
25.2
x + h – 2x
h26.
3x – h– 3
xh
27.2
x + h – 2x – h
h28.
3x + h–
h
3x – h