7.1 Rational Expressions and Functions;

8.5 Multiplying and Dividing Radical Expressions

Rational Function
A function of the form

is a rational function. Its domain consists of all real
numbers except those that make

Fundamental Property of Rational Numbers
If is a rational number and if cis any nonzero real
number, then

Writing a Rational Expression in Lowest Terms

Step 1 Factor the numerator and the denominator
completely.

Step 2 Apply the fundamental property. Divide out
common factors.

Multiplying Rational Expressions

Step 1 Factor numerators and denominators.

Step 2 Apply the fundamental property.

Step 3 Multiply the numerators and multiply the deno-
minators.

Step 4 Check that the product is in lowest terms.

Dividing Rational Expressions
Multiply the first rational expression (the dividend) by
the reciprocal of the second (the divisor).

a

b



ac

bc

.

a

b

Q 1 x 2 =0.

ƒ 1 x 2  whereQ 1 x 2 Z0,

P 1 x 2

Q 1 x 2

,

Find the domain.

Solve to find This is the only real number

excluded from the domain. The domain is

Write in lowest terms.

Factor.

Lowest terms

Multiply.

Factor.

Multiply; lowest terms

Divide.

Multiply by the reciprocal.

Factor.

= Multiply; lowest terms

x+ 3

x- 1

=

2 x+ 5

x- 3

#

1 x+ 321 x- 32

12 x+ 521 x- 12

=

2 x+ 5

x- 3

x

(^2) - 9
2 x^2 + 3 x- 5
2 x+ 5
x- 3

,

2 x^2 + 3 x- 5

x^2 - 9

=

5

31 x- 12

=

1 x+ 122

1 x- 121 x+ 12

#^5

31 x+ 12

x^2 + 2 x+ 1

x^2 - 1

#^5

3 x+ 3

=

2

x- 4

=

21 x+ 42

1 x- 421 x+ 42

2 x+ 8

x^2 - 16

3

4

=

3 # 5

4 # 5

=

15

20

5 x|xZ- 26.

3 x+ 6 = 0 x=-2.

ƒ 1 x 2 =

2 x+ 1

3 x+ 6

QUICK REVIEW

CONCEPTS EXAMPLES

(continued)

CHAPTER 7 Summary 417