Easy Algebra Step-by-Step

Rational Expressions 151

Complex Fractions

A complex fraction is a fraction that has fractions in its numerator, denomi-

nator, or both. One way you can simplify a complex fraction is to interpret

the fraction bar of the complex fraction as meaning division.

Problem Simplify

11

11

xy

x y

+

–

.

Solution

Step 1. Write the complex fraction as a division problem.

11

11

x y

xy

+

–

= +

⎛

⎝

⎛⎛

⎝⎝

⎞

⎠⎟

⎞⎞

⎠⎠

÷

⎛

⎝⎜

⎛⎛

⎝⎝

⎞

⎠⎟

⎞⎞

⎠⎠

(^11) + 11
xy x–y
Step 2. Perform the indicated addition and subtraction.

=

⎛ +

⎝⎜

⎛⎛

⎝⎝

⎞

⎠⎟

⎞⎞

⎠⎠

÷⎛

⎝⎜

⎛⎛

⎝⎝

⎞

⎠⎟

⎞⎞

⎠⎠

yx+

xy

yx−

xy

Step 3. Multiply by the reciprocal of the divisor.

=

( + )

⋅

( )

yx+

xy

xy

yx−

=

( + )

⋅

( )

yx+

xyxy

xyxy

yx−

=

( + )

( )

yx+

yx−