6.2 – rational expressions
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6.2 – Rational Expressions. Adding and Subtracting. What is the Lowest Common Denominator (LCD)?. 6.2 – Rational Expressions. Adding and Subtracting. What is the Lowest Common Denominator (LCD)?. 6.2 – Rational Expressions – Add. And Sub. What is the Lowest Common Denominator (LCD)?. - PowerPoint PPT PresentationTRANSCRIPT
6.2 – Rational ExpressionsAdding and Subtracting
65
32 and
What is the Lowest Common Denominator (LCD)?
21
72,
43 and
3 5
5 13andx x
4 2
17 34 6
andy y
6 28
5x 12 4y
57
53
aaand
aa
What is the Lowest Common Denominator (LCD)?
1235
47
2
2
xxand
xx
5a
3
27x and 5x
4x 4x
243 x
4x 4x 3 4x 5a
6.2 – Rational ExpressionsAdding and Subtracting
233
325
22
yyyand
yyy
What is the Lowest Common Denominator (LCD)?
1y
5y
3y 2y
3y 1y and 3y
1y 2y
6.2 – Rational Expressions – Add. And Sub.
737
733
xxx
Examples (Like Denominators):
1
3 7x 3x 7
6.2 – Rational Expressions – Add. And Sub.
264
252 2
xx
xxx
Examples (Like Denominators):
2x 22 5
2x x
x
22
2xx
2x
32 x22 5x x 4 6x
4x 6
x 6
2x 2 3x
6.2 – Rational Expressions – Add. And Sub.
6572
6513
22
xx
xxx
x
Examples (Like Denominators):
65
72132
xxxx
6513
2
xxx x2 7
656
2 xx
x
6x
x 1 x 6
11x
1
1
6.2 – Rational Expressions – Add. And Sub.
Examples:
153
5yy
LCD 15
153
5yy
33
153
153 yy
15
33 yy 150 0
6.2 – Rational Expressions – Add. And Sub.
Examples:
21011
85
xx
LCD 40x2
21011
85
xx
xx
55
22 4044
4025
xxx
2401125xx
44
6.2 – Rational Expressions – Add. And Sub.
Examples:
12
75
xx
LCD
5 27 1x x
7 1 7 1x x x x
7 1x x
7x 1x
11
xx
77xx
5x 5 14x 19x 5
6.2 – Rational Expressions – Add. And Sub.
35
9102
xxx
Examples:
10x
10 53 3 3x
x x x
103 3x
x x
3 3x x
3 3x x
3 3x x
35x
3x 3x
LCD
33
xx
3 3x x 5x 15
10x 155x
5x 15
5 3x 3x 3x
53x
6.2 – Rational Expressions – Add. And Sub.
8123
234
2
xx
xx
Examples:
LCD
4
4 3
3 2 4 3 2x
x x x
x 3 2x 3x
4 3 2x
4 x 3 2x
44
xx
6.2 – Rational Expressions – Add. And Sub.
Examples: continued
4 3 2 4 3 2x x x x
4 3 2x x
xx
xx
xx 2343
234
44
16 23x
216 3x
6.2 – Rational Expressions – Add. And Sub.
4446
22
xx
xxx
Examples:
6x x
LCD
6
2 2 2 2x x
x x x x
2x 2x 2x 2x
2x 2x 2x
22
xx
22
xx
6.2 – Rational Expressions – Add. And Sub.
Examples: continued
22
22226
22
xx
xxx
xxx
xx
2 2 2 2 2 2x x x x x x
2222126 22
xxx
xxxx
2 2 2x x x 22 2x x
26x 12x2x 2x
27x 10x x 7x 10
6.2 – Rational Expressions – Add. And Sub.
Defn: A rational expression whose numerator, denominator, or both contain one or more rational expressions.
7
5
yx
xyyx
873
4 3
1
1
xx
x
6.3 – Simplifying Complex FractionsComplex Fractions
3 24 31 32 8
3 24 31 32 8
3 43 4
4
3 24 3
1 384 2
24 24
2
3 24 314 32 8
24
9 812 12
4 38 8
6 3 8 212 1 3 3
11278
18 1612 9
221
221
LCD: 12, 8 LCD: 24
6.3 – Simplifying Complex Fractions
24
87
121
78
121
2
3
24
LCD: y1
2 1
xy
xy
1
2 1
y y
y
xy
xy
2 1y xx
yxyx
12
1y–y
6.3 – Simplifying Complex Fractions
LCD: 6xy
56
3
yy xy x
2
2 2
5 62 6x yxy x y
56
3
6 6
6 6
yy x
xy xy
y y xx xy
25 6x y2xy 3y x
xyxy
y
3
65
6xy
6.3 – Simplifying Complex Fractions
6xy
LCD:
3759
3759
3 57 9
63 37
63 59
3 97 5
9 37 5
2735
2735
63
Outers over Inners6.3 – Simplifying Complex Fractions
3759
2735
)5)(7()9)(3(
Outers over Inners
512
56
x
xx
512
56xxx
52
5xxx
6.3 – Simplifying Complex Fractions