Complex Rational Expressions

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Section 6.3

• Complex Rational Expressions

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What is a complex Rational Expression?

• If you have a sum/difference of rational
  expressions in the numerator or denominator of a
  quotient.
• How do I simplify one?
• Get it to just be a polynomial over a polynomial
• 2 options
• Simplify top and bottom separately
• Simplify by finding a least common denominator

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Method I simplify separately

• Treat numerator and denominator individually,
  simplify
• Write numerator as a single rational expression
• Write denominator as a single rational expression
• Rewrite original expression
• Simplify using techniques for dividing rational
  expressions (multiply by reciprocal!)

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Examples
Domain restrictions on each?
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Method II Using LCD

• Find the LCD among ALL the denominators.
• Multiply numerator AND denominator by the LCD.
• Simplify

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Examples Method II
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Examples with negative exponents

• Note You cannot move a term with a negative
  exponent from top to bottom (or vice versa) if it
  is part of a sum or difference.
• Key rewrite as a complex rational expression,
  use Method I or II