Section 8.2: Multiplying and Dividing Rational

Expressions

8.2 Lecture Guide: Multiplying and Dividing Rational Expressions

Objective: Multiply and divide rational expressions.

Multiplying Rational Expressions

Algebraically

and

Verbally

1. Factor the numerators and the denominators. Then write the product as a single fraction, indicating the product of the numerators and the product of the denominators.

If A, B, C and D are real polynomials and 0B 0D A C AC

B D BD then

2. Reduce this fraction by dividing the numerator and the denominator by any common nonzero factors.

Algebraic Example 2 5 4

4 12 2 10

x x y

xy xy x

Dividing Rational Expressions:

Algebraically and

Verbally

1. Rewrite the division problem as the product of the dividend and the reciprocal of the divisor.

If A, B, C and D are real polynomials and 0, 0B C 0D then

2. Perform the multiplication using the rule for multiplying rational expressions.

A C A D

B D B CAD

BC

Algebraic Example 20 5

3 27 4 36

a a

a a

Perform the indicated operations and reduce all results to lowest terms. Assume the variables are restricted to values that prevent division by zero.

1.25 5 25

15 7 7

x y x

x y x

2.2

2 2

3 4 4

4 6

x x x

x x x

3.2

2

35 7

3 24 56

x x

x x x

4.2

2

16 4

49 7

x x

x x

5.2 3

2

4 16 64

2 6 12

x x x

x x x

6.2 2

2 2

6 8 30 2 17 21

3 13 56 24 4 60

x x x x

x x x x

7.2 2 2

3 2 2

42 5 6 36

3 4 1 3 12

x x x x x

x x x x x

8.2 7 3 5

2 2 2 2

32 25 125 48

4 5

x y x y x y

x y x y x xy y

9.2 3 2

2 2

49 25 50

2 9 35 4 40 3 70

x x x

x x x x x

Determine the unknown expression in each equation.

10. 2

2

5 2 3?

2 3 2 3

x x x

x x x

Determine the unknown expression in each equation.

11. 2

2

6 11 3 3 1?

6 13 5 3 1

x x x

x x x