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 48: 70



Work Step by Step

The given expression, $ \dfrac{y+\dfrac{1}{y^2-9}}{\dfrac{1}{y+3}} ,$ simplifies to \begin{array}{l}\require{cancel} \dfrac{\dfrac{y(y^2-9)+1(1)}{y^2-9}}{\dfrac{1}{y+3}} \\\\= \dfrac{\dfrac{y^3-9y+1}{y^2-9}}{\dfrac{1}{y+3}} \\\\= \dfrac{y^3-9y+1}{y^2-9}\div\dfrac{1}{y+3} \\\\= \dfrac{y^3-9y+1}{y^2-9}\cdot\dfrac{y+3}{1} \\\\= \dfrac{y^3-9y+1}{(y+3)(y-3)}\cdot\dfrac{y+3}{1} \\\\= \dfrac{y^3-9y+1}{(\cancel{y+3})(y-3)}\cdot\dfrac{\cancel{y+3}}{1} \\\\= \dfrac{y^3-9y+1}{y-3} .\end{array}
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