Write as a division problem.

Multiply by the reciprocal of. (Step 2)

Multiply and simplify. (Step 3)

NOW TRY

=

2 y+ 1

3 y- 2

3 y- 2

= y

2 y+ 1

y

y

3 y- 2

=

2 y+ 1

y

,

3 y- 2

y

2 y+ 1

y

3 y- 2

y

=

SECTION 7.3 Complex Fractions 381

The numerator is a

single fraction. So is

the denominator.

OBJECTIVE 2 Simplify complex fractions by multiplying by a common

denominator (Method 2).This method uses the identity property for multiplication.

Simplifying Complex Fractions (Method 2)

Use Method 2 to simplify each complex fraction.

(a)

Identity property of multiplication

a 2 +

1

y

b #y

a 3 -

2

y

b #y

=

1

2 +

1

y

3 -

2

y

=

2 +

1

y

3 -

2

y

EXAMPLE 2

The LCD of all the fractions is y.

Multiply the numerator and denominator

by y, since (Step 1)

y

y=1.

This is the same fraction as

in Example 1(b).Compare

the solution methods.

NOW TRY
EXERCISE 1
Use Method 1 to simplify
each complex fraction.

(a) (b)

5 -

2

y

4 +

1

y

t+ 4

3 t

2 t+ 1

9 t

NOW TRY ANSWERS

1. (a)^312 tt++ 142 (b) 45 yy+- 12

Simplifying a Complex Fraction (Method 2)

Step 1 Multiply the numerator and denominator of the complex fraction by

the least common denominator of the fractions in the numerator and

the fractions in the denominator of the complex fraction.

Step 2 Simplify the resulting fraction if possible.

Distributive property (Step 2)

= Multiply.

2 y+ 1

3 y- 2

2 #y+

1

y

#y

3 #y-

2

y

#y

=