6.2 – rational expressions

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