Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 6 - Section 6.2 - Adding and Subtracting Rational Expressions - Exercise Set: 82

Answer

$\dfrac{7x-15}{x(x+1)(x-3)}$

Work Step by Step

The given expression, $ \dfrac{1}{x+1}\cdot\left( \dfrac{5}{x}+\dfrac{2}{x-3} \right) ,$ simplifies to \begin{array}{l}\require{cancel} \dfrac{1}{x+1}\cdot\dfrac{(x-3)(5)+x(2)}{x(x-3)} \\\\= \dfrac{1}{x+1}\cdot\dfrac{5x-15+2x}{x(x-3)} \\\\= \dfrac{1}{x+1}\cdot\dfrac{7x-15}{x(x-3)} \\\\= \dfrac{7x-15}{x(x+1)(x-3)} .\end{array}
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