11-7 Rational Expressions with Unlike Denominators

Algebra 1 Glencoe McGraw-Hill Linda Stamper

As with fractions, to add or subtract rational expressions with unlike, or different denominators, you must rewrite with a common denominator before adding or subtracting.

83

21

21

83

44

84

83

87

x2

2x

2x1x2

2x

2x1

22 x

2x1

x

2x

2x

2x12x

x1

2

2m

2m33m2

3m2

2m

2m3

23m

2m23m

m69

23m

m69m2

3m

9m4 2

xx

mm

33

3m

9m41 2

3m

9m4 2

You must place the

subtracted quantity in

parentheses!

The problem.216x

x420x3

Write the denominators as prime factors.

x5223

Multiply numerator and denominator by factors needed to create a common denominator.

x22x22

55

Multiply to write the expression with a common denominator. Simplify.

xx2222

x4

x5223

xx2222x4

280x12x

280x

x52012x

280x

x52012x

80x

2017x 2

280x

x520

You must place the

subtracted quantity in

parentheses!

The problem.216x

x420x3

Write the denominators as factors. x54

3

Multiply numerator and denominator by factors needed to create a common denominator.

x4x4 5

5

Multiple to write the expression with a common denominator. Simplify.

xx44

x4

x543

xx44x4

280x

12x280x

x520

280x

x52012x

280x

x52012x

80x

2017x 2

Write in simplest form.

x2

x

12

2x

1x2 x

x

22 x

2x

x

1

2x

2x1

x

12x 2

Example 1

Example 2

32 9x

1

15x

3

xx533

xx533

3x3x

xxx331

55

345x

9x345x

5

45x

59x 3

xxx331

Example 3

28x

1x6x7

x327

x327 x22

x22

xx2221x

33

224x28x

224x

3x3

xx222

1x

224x

33x28x

224x

3x328x

24x

325x 2

Write in simplest form. Example

41x

11x

1

1x1

1x

1x 1x

1

1x

1x

1x1x

1x1x

1x1xx2

Example 5

x1

6x3

6x3 x

xx1

6x

6x

6xx3x 6xx

6x

6xx6x3x

6xx64x

6xx32x2

Write in simplest form. Example

62x2x

5x5x

5x

5x

2x2x

2x2x

5x5x

2x5x10x7x2

2x5x10x7x2

2x5x

10x7x10x7x 22

2x5x10x7x10x7x 22

2x5xx14

2x5xx14

Example 7 Write in simplest form.

23 10x

1

4x

4x3

xxx22

4x3

55

xx521

xxx22

4x3

xx52

1

x2x2

3x20

x20153x02

2x

3x20

15x18

x20

5x63 3

11-A6 Page 617-619 # 22–39,43-46,57,64-65.