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10/24/2015 1 Simplifying, Multiplying and Dividing Rational Expressions

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10/24/2015 2 Simplifying Rational Expressions Let a, b, and c be nonzero real numbers (or variable expressions). Then,

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10/24/2015 3 Example: Simplify Factor the numerator and denominator Cancel common factors Rewrite the simplified expression

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10/24/2015 4 Example: Simplify

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10/24/2015 5 Multiplying Rational Expressions with Monomials Simplify as much as possible Multiply numerators Multiply denominators Simplify Rewrite the simplified expression

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10/24/2015 6 Example: 2 5 3

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10/24/2015 7 Multiplying Rational Expressions with polynomials Factor the numerators and denominators of each rational expression Simplify by dividing out common factors Multiply Rewrite in simplified form (no parentheses or negative exponents)

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10/24/2015 8 Example:

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10/24/2015 9 Dividing Rational Expressions Rewrite as a multiplication problem (Multiply the first by the reciprocal of the second.) Factor numerators and denominators Simplify Multiply Rewrite the answers in simplified form

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10/24/2015 10 Example:

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10/24/2015 11 Multiplying or Dividing Rational Expressions by Polynomials Treat the denominator of the polynomial expression as 1. Factor each numerator and denominator Multiply/”Divide” Rewrite in simplified form

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10/24/2015 12 Example

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10/24/2015 13 Assignment Page 558 #16-49

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