(b)

Factor.

Fundamental property

(c)

Write as

Factor.

Fundamental property

(d)

Factor.

Multiply; lowest terms

(e)

Factor.

= Lowest terms NOW TRY

1

x+ 4

=

x- 6

1 x- 622

1 x+ 321 x- 62

1 x+ 321 x+ 42

x- 6

x^2 - 12 x+ 36

#x

(^2) - 3 x- 18

x^2 + 7 x+ 12

=

1 x+ 221 x- 12

x 1 x+ 12

=

x 1 x+ 22

x+ 1

1 x+ 121 x- 12

x^21 x+ 12

x^2 + 2 x

x+ 1

x

(^2) - 1

x^3 + x^2

=

3

5

=

p- 4

1

#^3

51 p- 42

p 4

= p 4 1.

p- 4

1

#^3

5 p- 20

1 p- 42 #

3

5 p- 20

=

k

k- 4

k 1 k- 12

1 k+ 521 k- 42

=

1 k+ 521 k- 32

1 k- 321 k- 12

k^2 + 2 k- 15

k^2 - 4 k+ 3

k

(^2) - k

k^2 + k- 20

SECTION 7.1 Rational Expressions and Functions; Multiplying and Dividing 367

Remember to include

1 in the numerator

when all other factors

are eliminated.

NOW TRY
EXERCISE 4
Multiply.

(a)

(b)

m^2 + 2 m- 15

m^2 - 5 m+ 6

m

(^2) - 4
m^2 + 5 m
8 t^2
t^2 - 4
#^3 t+^6
9 t
NOW TRY ANSWERS

4. (a) 31 t^8 - t 22 (b)mm+^2

OBJECTIVE 5 Find reciprocals of rational expressions.The rational numbers

and are reciprocals of each other if they have a product of 1. The reciprocalof a

rational expression is defined in the same way: Two rational expressions are recip-

rocals of each other if they have a product of 1. Recall that 0 has no reciprocal.

The table shows several rational expressions and their reciprocals.

c

d

a

b

OBJECTIVE 6 Divide rational expressions.

Reciprocals have a product

of 1.

Rational

Expression Reciprocal

3, or

undefined

0

4

2

m^2 - 9 m

m^2 - 9 m

2

k

5

5

k

1

3

3

1

Finding the Reciprocal

To find the reciprocal of a nonzero rational expression, interchange the nu-

merator and denominator of the expression.

Dividing Rational Expressions

To divide two rational expressions, multiplythe first (the dividend) by the

reciprocal of the second (the divisor).