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Section 9.4

Section 9.4. Multiplying and Dividing Rational Expressions. Multiplying and Dividing Rational Expressions. Factor the numerator and denominator. Example: Simplify. Cancel common factors.

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Section 9.4

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  1. Section 9.4 Multiplying and Dividing Rational Expressions

  2. Multiplying and Dividing Rational Expressions Factor the numerator and denominator... Example:Simplify Cancel common factors... A rational expression is considered to be simplified when its numerator and denominator have no common factors left… 2x Reduce...

  3. Multiplying Fractions (Parenthesize polynomials for clarity) To Simplify: Factor, then cancel like factors

  4. Example – Step by Step x 1 1 4 1 1 Write down original problem Combine with parenthesized polynomials Factor polynomials (if possible) Rewrite (if any factoring was done) Cancel out matching factors Simplify the answer

  5. Practice - Rational Multiplication • Write down original problem • Combine with parenthesized polynomials • Factor polynomials (if possible) • Rewrite (if any factoring was done) • Cancel out matching factors • Simplify the answer

  6. Practice - Rational Multiplication • Write down original problem • Combine with parenthesized polynomials • Factor polynomials (if possible) • Rewrite (if any factoring was done) • Cancel out matching factors • Simplify the answer

  7. Practice - Rational Multiplication • Write down original problem • Combine with parenthesized polynomials • Factor polynomials (if possible) • Rewrite (if any factoring was done) • Cancel out matching factors • Simplify the answer

  8. Multiplying rational expressions works the same as multiplying fractions…you may multiply numerators and denominators and then simplify, or you can cross cancel common factors... Example:Multiply With monomials, it’s a good idea to multiply first, and then simplify... Now reduce... 4 3 4y3 3

  9. With polynomials, factor each numerator and denominator, if factorable, and cross cancel to simplify... Example:Multiply Factor... Cross cancel... x + 1 x

  10. Example:Divide Rewrite as multiplication... Recall that to divide fractions, you can “invert and multiply: ... Factor... Cross cancel... = 6x2 3x = 2x

  11. Finding Powers of Rational Expressions • Factor and Simplify (if possible) before applying the power • If part of a larger expression, see if any terms cancel out • Usually leave in factored form (unlike the text example)

  12. Dividing Fractions Change to multiplication by reciprocal, then follow the procedure for multiplication

  13. Practice - Rational Division • Write down original problem1a. Rewrite as multiplication by reciprocal • Combine with parenthesized polynomials • Factor polynomials (if possible) • Rewrite (if any factoring was done) • Cancel out matching factors • Simplify the answer

  14. Practice - Rational Division • Write down original problem1a. Rewrite as multiplication by reciprocal • Combine with parenthesized polynomials • Factor polynomials (if possible) • Rewrite (if any factoring was done) • Cancel out matching factors • Simplify the answer

  15. Practice - Rational Division • Write down original problem1a. Rewrite as multiplication by reciprocal • Combine with parenthesized polynomials • Factor polynomials (if possible) • Rewrite (if any factoring was done) • Cancel out matching factors • Simplify the answer

  16. Mixed Operations • Multiplications & Division are done left to right • In effect, make each divisor into a reciprocal

  17. Assignment Section 9.4: page 558 – 559 # 18 – 48 (every 3rd)

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