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: 58

Answer

$\dfrac{(x+2)(x-3)}{9}$

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^2-4}{9}\cdot\dfrac{x^2-6x+9}{x^2-5x+6} $, simplifies to \begin{array}{l}\require{cancel} \dfrac{(x+2)(x-2)}{9}\cdot\dfrac{(x-3)(x-3)}{(x-3)(x-2)} \\\\= \dfrac{(x+2)(\cancel{x-2})}{9}\cdot\dfrac{(\cancel{x-3})(x-3)}{(\cancel{x-3})(\cancel{x-2})} \\\\= \dfrac{(x+2)(x-3)}{9} .\end{array}
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