College Algebra (11th Edition)

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

Chapter R - Review Exercises - Page 76: 86



Work Step by Step

The given expression, $ \dfrac{3+\dfrac{2m}{m^2-4}}{\dfrac{5}{m-2}} ,$ simplifies to \begin{array}{l}\require{cancel} \dfrac{\dfrac{3(m^2-4)+2m}{m^2-4}}{\dfrac{5}{m-2}} \\\\= \dfrac{\dfrac{3m^2-12+2m}{m^2-4}}{\dfrac{5}{m-2}} \\\\= \dfrac{3m^2+2m-12}{m^2-4}\div\dfrac{5}{m-2} \\\\= \dfrac{3m^2+2m-12}{(m+2)(m-2)}\cdot\dfrac{m-2}{5} \\\\= \dfrac{3m^2+2m-12}{(m+2)(\cancel{m-2})}\cdot\dfrac{\cancel{m-2}}{5} \\\\= \dfrac{3m^2+2m-12}{5(m+2)} .\end{array}
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