1. § 7.7 Simplifying Complex Fractions

2. 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.

3. Martin-Gay, Beginning and Intermediate Algebra, 4ed 33 Method 1: Simplifying a Complex Fraction 1) 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

4. Martin-Gay, Beginning and Intermediate Algebra, 4ed 44 Simplifying Complex Fractions Example:

5. Martin-Gay, Beginning and Intermediate Algebra, 4ed 55 Method 2: Simplifying a Complex Fraction 1) 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

6. Martin-Gay, Beginning and Intermediate Algebra, 4ed 66 Simplifying Complex Fractions Example: