(b)

Distributive property (Step 2)

Multiply.

Multiply again.

This rational expression is in lowest terms. NOW TRY

=

2 p^3 - 2 p^2 + 5 p

3 p^3 - 3 p^2 - 2 p+ 2

=

2 p 3 p 1 p- 124 + 5 p

3 p 3 p 1 p- 124 - 21 p- 12

2 p 3 p 1 p- 124 +

5

p- 1

#p 1 p- 12

3 p 3 p 1 p- 124 -

2

p

#p 1 p- 12

=

a 2 p+

5

p- 1

b #p 1 p- 12

a 3 p-

2

p

b #p 1 p- 12

=

2 p+

5

p- 1

3 p-

2

p

382 CHAPTER 7 Rational Expressions and Functions

Multiply the numerator and

denominator by the LCD,

p 1 p- 12 .(Step 1)

OBJECTIVE 3 Compare the two methods of simplifying complex fractions.

In the next example, we illustrate how to simplify a complex fraction by both

methods. Some students prefer one method over the other, while other students feel

comfortable with both methods and rely on practice with many examples to determine

which method they will use on a particular problem.

Simplifying Complex Fractions (Both Methods)

Use both Method 1 and Method 2 to simplify each complex fraction.

EXAMPLE 3

Method 1

(a)

=

21 x+ 32

5

=

2

x- 3

1 x- 321 x+ 32

5

=

2

x- 3

,

5

1 x- 321 x+ 32

2

x- 3

5

1 x- 321 x+ 32

=

2

x- 3

5

x^2 - 9

Method 2

(a)

=

21 x+ 32

5

2

x- 3

1 x- 321 x+ 32

5

1 x- 321 x+ 32

1 x- 321 x+ 32

=

2

x- 3

5

1 x- 321 x+ 32

=

2

x- 3

5

x^2 - 9

NOW TRY
EXERCISE 2
Use Method 2 to simplify each
complex fraction.

(a) (b)

x+

5

x

4 x-

1

x- 2

5 -

2

y

4 +

1

y

NOW TRY ANSWERS

2. (a)

(b)

x^3 - 2 x^2 + 5 x- 10

4 x^3 - 8 x^2 - x

5 y- 2

4 y+ 1