Beginning Algebra, 11th Edition

SECTION 7.2 Multiplying and Dividing Rational Expressions 429

OBJECTIVES

Multiplying and Dividing Rational Expressions

7.2

1 Multiply rational

expressions.

2 Divide rational

expressions.

OBJECTIVE 1 Multiply rational expressions.The product of two fractions is

found by multiplying the numerators and multiplying the denominators. Rational ex-

pressions are multiplied in the same way.

Remember to

write 1 in the

numerator.

Multiplying Rational Expressions

The product of the rational expressions and is defined as follows.

That is, to multiply rational expressions, multiply the numerators and multiply

the denominators.

P

Q

#R

S



PR

QS

R

S

P

Q

Multiplying Rational Expressions

Multiply. Write each answer in lowest terms.

(a) (b)

Indicate the product of the numerators and the product of the denominators.

Leave the products in factored form because common factors are needed to write the

product in lowest terms. Factor the numerator and denominator to further identify any

common factors. Then use the fundamental property to write each product in lowest

terms.

= NOW TRY

x

2

=

1

6

=

6 #x#x

2 # 6 #x

=

3 # 5

2 # 5 # 3 # 3

=

6 #x^2

x# 12

=

3 # 5

10 # 9

6

x

#x

2

12

3

10

#^5

9

EXAMPLE 1

NOTE It is also possible to divide out common factors in the numerator and denom-

inator beforemultiplying the rational expressions. Consider this example.

Identify the common factors.

Divide out the common factors.

= Multiply.

21

11

=

3

1

#^7

11

=

2 # 3

5

#^5

# 7

2 # 11

6

5

#^35

22

NOW TRY
EXERCISE 1
Multiply. Write the answer in
lowest terms.

4 k^2

7

#^14

11 k

NOW TRY ANSWER

1.^811 k