Complex Rational Expressions

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Complex Rational Expressions

• Section 6.4

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What is a complex fraction?
A complex fraction is a rational expression that
has a fraction in its numerator, denominator or
both. In other words, there is at least one
small fraction within the overall fraction. Some
examples of complex fractions are
and
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Method I Simplifying a Complex Fraction

• Step 1 If needed, rewrite the numerator and
  denominator so that they are each a single
  fraction.
• Combine all the parts of the numerator to
  form one fraction and all of the parts of the
  denominator to form another fraction.
• Step 2 Divide the numerator by the denominator
  by multiplying the numerator by the reciprocal of
  the denominator.
• Step 3 If needed, simplify the rational
  expression.

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Example 1

• Step 1 Rewrite the numerator and denominator
  so that they are each a single fraction.

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Example 2

• Rewrite fractions with LCD of ab.

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Method II Simplifying a Complex Fraction

• Step 1 Multiply the numerator and denominator of
  the overall complex fractions by the LCD of the
  smaller fractions.
• Recall that when you multiply the exact same
  thing to the numerator and the denominator, the
  result is an equivalent fraction.
• Step 2 If needed, simplify the rational
  expression.

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Example 3

• Step 1 Multiply the numerator and denominator by
  the LCD of the smaller fractions.

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Step 2. Simplify the rational expression.
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Example
What is the LCD of a, b, and ab2?
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Example
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Example
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Example