Intermediate Algebra (11th edition)

As shown in Example 3,the quotient can be simplified.

The following statement summarizes this result.

a

- a

=

a

- 11 a 2

=

1

- 1

=- 1

a

- a^1 aZ^02

366 CHAPTER 7 Rational Expressions and Functions

Quotient of Opposites

In general, if the numerator and the denominator of a rational expression are

opposites, then the expression equals -1.

Numerator and denominator

are notopposites.

Multiplying Rational Expressions

Multiply.

(a)

Factor.

Commutative property

Fundamental property

= Lowest terms

3 p

2

=

1

1

#^1

1

#^1

1

#^3 p

2

=

51 p- 12

51 p- 12

#p

p

#^3 p

2

=

51 p- 12

p

#^3 p

#p

2 # 51 p- 12

5 p- 5

p

#^3 p

2

10 p- 10

EXAMPLE 4

Based on this result, the following are true statements.

and

Numerator and denominator in each expression are opposites.

However, the following expression cannot be simplified further.

OBJECTIVE 4 Multiply rational expressions.To multiply rational expressions,

follow these steps. (In practice, we usually simplify before multiplying.)

r- 2

r+ 2

- 5 a+ 2 b

5 a- 2 b

=- 1

q- 7

7 - q

=- 1

Multiplying Rational Expressions

Step 1 Factorall numerators and denominators as completely as possible.

Step 2 Apply the fundamental property.

Step 3 Multiplythe numerators and multiply the denominators.

Step 4 Checkto be sure that the product is in lowest terms.