Intermediate Algebra (11th edition)

380 CHAPTER 7 Rational Expressions and Functions

OBJECTIVES A complex fractionis a quotient having a fraction in the numerator, denominator, or

both.

, , and Examples of complex fractions

OBJECTIVE 1 Simplify complex fractions by simplifying the numerator

and denominator (Method 1).

m^2 - 9

m+ 1

m+ 3

m^2 - 1

4

y

6 -

3

y

1 +

1

x

2

Complex Fractions

7.3

1 Simplify complex

fractions by

simplifying the

numerator and

denominator

(Method 1).

2 Simplify complex

fractions by

multiplying by

a common

denominator

(Method 2).

3 Compare the two

methods of

simplifying complex

fractions.

4 Simplify rational

expressions with

negative exponents.

Before performing Step 2, be sure that both numerator and denominator are

single fractions.

Simplifying Complex Fractions (Method 1)

Use Method 1 to simplify each complex fraction.

(a)

Write as a division problem.

Multiply by the reciprocal of. (Step 2)

Multiply.

= Simplify. (Step 3)

21 x+ 12

x- 1

=

2 x 1 x+ 12

x 1 x- 12

x- 1

= 2 x

x+ 1

x

#^2 x

x- 1

=

x+ 1

x

,

x- 1

2 x

x+ 1

x

x- 1

2 x

EXAMPLE 1

Both the numerator and the denominator

are already simplified. (Step 1)

Simplifying a Complex Fraction (Method 1)

Step 1 Simplify the numerator and denominator separately.

Step 2 Divide by multiplying the numerator by the reciprocal of the

denominator.

Step 3 Simplify the resulting fraction if possible.

(b)

2 y

y

+

1

y

3 y

y

-

2

y

=

2 +

1

y

3 -

2

y

Simplify the numerator and

denominator separately. (Step 1)

Prepare to write the numerator

and denominator as single fractions.