Adding and Subtracting Rational Expressions

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Section 7.2

• Adding and Subtracting Rational Expressions

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Overview

• In this section we will examine how to add and
  subtract rational expressions.
• Since rational expressions are a special type of
  fraction, the same requirements are in place for
  adding and subtracting them.
• That is, a COMMON DENOMINATOR is required.

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Case I You have a common denominator

• Add or subtract the terms in the numerator.
• Be prepared to have to reduce to lowest terms by
  first factoring the numerator and denominator and
  them canceling common factors.
• Remember, you cannot cancel terms.

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Examples
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Case II You do not have a common denominator

• How to find a least common denominator
• Factor each denominator.
• The LCD is the product of all the different
  factors from each denominator, with each factor
  raised to the greatest power that occurs in any
  denominator.

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Lets Practice, Shall We?

• Find the LCD for each group of denominators

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Continued

• After you find your LCD, you must re-build your
  denominators to match your LCD.
• Whatever factors you add to the denominator,
  you must add the same factors to the numerator.
• FOIL, distribute, multiply as needed in the
  numerator, then combine like terms.

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Still Not Finished!

• Dont forget to check and see whether your
  rational expression can be reduced to lowest
  terms.
• IMPORTANT the cancelling of factors comes last
  in this process!
• Remember, you cannot cancel terms.

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All Together NowAdd or Subtract
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More Examples