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Chapter 6
Rational Expressions, Equations, and Functions
Copyright © Cengage Learning. All rights reserved.

2. Copyright © Cengage Learning. All rights reserved.
6.4 Complex Fractions
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3. What You Should Learn
Simplify complex fractions using rules for dividing rational expressions.
Simplify complex fractions having a sum or difference in the numerator and/or denominator.

4. Complex Fractions

5. Complex Fractions
Problems involving the division of two rational expressions are sometimes written as complex fractions.
A complex fraction is a fraction that has a fraction in its numerator or denominator, or both.
The rules for dividing rational expressions still apply.
For instance, consider the following complex fraction.

6. Complex Fractions
To perform the division implied by this complex fraction, invert the denominator fraction (the divisor) and multiply, as follows.
Note that for complex fractions, you make the main fraction line slightly longer than the fraction lines in the numerator and denominator.

7. Example 1 – Simplifying a Complex Fraction
Invert divisor and multiply.
Multiply, factor, and divide out common factors.
Simplified form

8. Complex Fractions with Sums or Differences

9. Complex Fractions with Sums or Differences
Complex fractions can have numerators and/or denominators that are sums or differences of fractions.
One way to simplify such a complex fraction is to combine the terms so that the numerator and denominator each consist of a single fraction.
Then divide by inverting the denominator and multiplying.

10. Example 5 – Simplifying a Complex Fraction
Add fractions. Rewrite with
least common denominators.
Invert divisor and multiply.
Simplified form

11. Complex Fractions with Sums or Differences
When simplifying a rational expression containing negative exponents, first rewrite the expression with positive exponents and then proceed with simplifying the expression.