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7.7

• Simplifying Complex Fractions

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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.

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Simplifying Complex Fractions

• 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.

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Simplifying Complex Fractions
Example
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Simplifying Complex Fractions

• 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.

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Simplifying Complex Fractions
Example