Math 101 Intermediate Algebra
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Complex Fractions
Chapter 7, Section 3


What is a Complex Fraction?

A complex fraction is a rational expression whose numerator and denominator are themselves rational expressions.

Since the numerator and denominator of the complex fraction are fractions themselves, the numerator and denominator are each called secondary fractions.


Simplifying Complex Fractions

The steps for 2 methods of simplifying complex fractions are given here.

Method 1:  Multiplying by a Common Denominator

  1. Find the lowest common denominator of the two secondary fractions.

  2. Multiply both the numerator and denominator of the complex fraction by this lowest common denominator.

  3. Simplify (reduce to lowest terms) the resulting rational expression.

Method 2:  Simplifying Numerator and Denominator

  1. Simplify (reduce to lowest terms) each secondary fraction.

  2. Simplify (reduce to lowest terms) the resulting rational expression by the dividing rational expressions method shown in section 7.1.