Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 6 - Section 6.1 - Rational Functions and Multiplying and Dividing Rational Expressions - Exercise Set - Page 346: 49

Answer

$\dfrac{4}{(x+2)(x+3)}$

Work Step by Step

Factoring the expressions and then cancelling the common factor/s between the numerator and the denominator, then the given expression, $ \dfrac{x^2-6x+9}{x^2-x-6}\div\dfrac{x^2-9}{4} $, simplifies to \begin{array}{l}\require{cancel} \dfrac{x^2-6x+9}{x^2-x-6}\cdot\dfrac{4}{x^2-9} \\\\= \dfrac{(x-3)(x-3)}{(x-3)(x+2)}\cdot\dfrac{4}{(x+3)(x-3)} \\\\= \dfrac{(\cancel{x-3})(\cancel{x-3})}{(\cancel{x-3})(x+2)}\cdot\dfrac{4}{(x+3)(\cancel{x-3})} \\\\= \dfrac{4}{(x+2)(x+3)} .\end{array}
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