Beginning Algebra, 11th Edition

Dividing Rational Expressions

Divide. Write the answer in lowest terms.

Multiply by the reciprocal.

Power rule for exponents

Multiply numerators.

Multiply denominators.

= Lowest terms

3

mp

=

9 # 16 m^2 p^2

8 # 6 p^3 m^3

=

9 m^2

8 p^3

#^16 p

2

6 m^3

=

13 m 22

12 p 23

#^16 p

2

6 m^3

13 m 22

12 p 23

,

6 m^3

16 p^2

EXAMPLE 5

SECTION 7.2 Multiplying and Dividing Rational Expressions 431

Dividing Rational Expressions

If and are any two rational expressions with then their quotient is

defined as follows.

That is, to divide one rational expression by another rational expression, multiply

the first rational expression (dividend) by the reciprocal of the second rational

expression (divisor).

P

Q



R

S



P

Q

#S

R



PS

QR

R

SZ0,

R

S

P

Q

Dividing Rational Expressions

Divide. Write each answer in lowest terms.

(a) (b)

Multiply the dividend by the reciprocal of the divisor.

Reciprocal of

=

10

7

=

y+ 5

41 y+ 32

=

5 # 8 # 2

8 # 7

=

y 1 y+ 52

1 y+ 3214 y 2

=

5 # 16

8 # 7

=

y

y+ 3

#y+^5

4 y

7

= 16

5

8

#^16

7

y

y+ 3

,

4 y

y+ 5

5

8

,

7

16

EXAMPLE 4

Reciprocal

of

4 y

y+ 5

NOW TRY

(2p)^3 = 23 p^3

(3m)^2 = 32 m^2 ;

The preceding discussion illustrates dividing common fractions. Division of

rational expressions is defined in the same way.

NOW TRY
EXERCISE 4
Divide. Write the answer in
lowest terms.

2 x- 5

3 x^2

,

2 x- 5

12 x

NOW TRY ANSWERS

4. 4
   x

NOW TRY
EXERCISE 5
Divide. Write the answer in
lowest terms.

13 k 23

2 j^4

,

9 k^2

6 j

5.

9 k

j^3 NOW TRY