College Algebra (11th Edition)

Published by Pearson
ISBN 10: 0321671791
ISBN 13: 978-0-32167-179-0

Chapter R - Section R.5 - Rational Expressions - R.5 Exercises - Page 47: 30



Work Step by Step

The given expression, $ \dfrac{6r-18}{9r^2+6r-24}\div\dfrac{4r-12}{12r-16} ,$ simplifies to \begin{array}{l}\require{cancel} \dfrac{6r-18}{9r^2+6r-24}\cdot\dfrac{12r-16}{4r-12} \\\\= \dfrac{6(r-3)}{(3r-4)(3r+6)}\cdot\dfrac{4(3r-4)}{4(r-3)} \\\\= \dfrac{6(\cancel{r-3})}{(\cancel{3r-4})(3r+6)}\cdot\dfrac{\cancel{4}(\cancel{3r-4})}{\cancel{4}(\cancel{r-3})} \\\\= \dfrac{6}{3r+6} \\\\= \dfrac{6}{3(r+2)} \\\\= \dfrac{\cancel{3}(2)}{\cancel{3}(r+2)} \\\\= \dfrac{2}{r+2} .\end{array}
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