§ 7.7

Simplifying Complex Fractions

Martin-Gay, Beginning and Intermediate Algebra, 4ed 22

Complex Rational Expressions

Complex rational expressions (complex fractions) are rational expressions whose numerator, denominator, or both contain one or more rational expressions.There are two methods that can be used when simplifying complex fractions.

Martin-Gay, Beginning and Intermediate Algebra, 4ed 33

Method 1: Simplifying a Complex Fraction1) Add or subtract fractions in the numerator and denominator

so that the numerator is a single fraction and the denominator is a single fraction.

2) Perform the indicated division by multiplying the numerator of the complex fraction by the reciprocal of the denominator of the complex fraction. Multiply the numerator of the complex fraction by the reciprocal of the denominator of the complex fraction.

3) Write the rational expression in simplest form.

Simplifying Complex Fractions

Martin-Gay, Beginning and Intermediate Algebra, 4ed 44

22

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24

2

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Simplifying Complex Fractions

Example:

Martin-Gay, Beginning and Intermediate Algebra, 4ed 55

Method 2: Simplifying a Complex Fraction1) Find the LCD of all the fractions in the complex

fraction.2) Multiply both the numerator and the denominator of

the complex fraction by the LCD in Step 1.3) Perform the indicated operations and write the result in

simplest form.

Simplifying Complex Fractions

Martin-Gay, Beginning and Intermediate Algebra, 4ed 66

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Simplifying Complex Fractions

Example: