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