Multiplying & Dividing Rational Expressions

MATH 018

Combined Algebra

S. Rook

2

Overview

• Section 7.2 in the textbook:– Multiply rational expressions– Divide rational expressions

3

Multiplying Rational Expressions

44

Multiplying Rational Expressions

• Consider multiplying 2/8 * 4/6

– Factor each numerator and denominator• i.e. write the prime factorization

– Divide out common factors between numerators and denominators

– Multiply across to get the final answer1/6

55

Multiplying Rational Expressions (Continued)

• Same process with rational expressions– Completely factor the numerator and

denominator of each fraction– Divide out common factors

• Remember for polynomials other than a monomial, divide out either EVERYTHING or NOTHING AT ALL

– Multiply the remaining factors for the final answer

Multiplying Rational Expressions (Example)

Ex 1: Multiply and simplify:

a)

b)

6

484

65

352

662

2

2

xx

xx

xx

x

352

50102

125

252

2

3

2

xx

xx

x

x

7

Dividing Rational Expressions

88

Dividing Rational Expressions

• Consider dividing 2/8 ÷ 4/6

– Convert into a multiplication problem by flipping the second fraction

– Factor each numerator and denominator– Divide out common factors between numerators

and denominators– Multiply to get the final answer

3/8

99

Dividing Rational Expressions (Continued)

• Same process with rational expressions– Convert into a multiplication problem by taking the

reciprocal of the second rational expression– Completely factor the numerator and denominator of

each fraction– Divide out common factors

• Remember for polynomials other than a monomial, divide out either EVERYTHING or NOTHING AT ALL

– Multiply the remaining products for the final answer

Dividing Rational Expressions (Example)

Ex 2: Divide and simplify:

a)

b)

c)

10

273

654

169

35122

2

2

2

pp

pp

pp

pp

3216

6

229

27 2

2

3

r

rr

rr

r

2

348

73

115

ac

cba

cb

ba

11

Summary

• After studying these slides, you should know how to do the following:– Multiply rational expressions– Divide rational expressions

• Additional Practice– See the list of suggested problems for 7.2

• Next lesson– Adding & Subtracting Rational Expressions

with the Same Denominator (Section 7.3)