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: 69

Answer

$\dfrac{m^2-5}{m-2}$

Work Step by Step

The given expression, $ \dfrac{m-\dfrac{1}{m^2-4}}{\dfrac{1}{m+2}} ,$ simplifies to \begin{array}{l}\require{cancel} \dfrac{\dfrac{(m^2-4)-1}{m^2-4}}{\dfrac{1}{m+2}} \\\\= \dfrac{\dfrac{m^2-5}{m^2-4}}{\dfrac{1}{m+2}} \\\\= \dfrac{m^2-5}{m^2-4}\div\dfrac{1}{m+2} \\\\= \dfrac{m^2-5}{m^2-4}\cdot\dfrac{m+2}{1} \\\\= \dfrac{m^2-5}{(m+2)(m-2)}\cdot\dfrac{m+2}{1} \\\\= \dfrac{m^2-5}{(\cancel{m+2})(m-2)}\cdot\dfrac{\cancel{m+2}}{1} \\\\= \dfrac{m^2-5}{m-2} .\end{array}
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