Intermediate Algebra (6th Edition)

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

Chapter 6 - Sections 6.1-6.5 - Integrated Review - Expressions and Equations Containing Rational Expressions - Page 380: 11

Answer

$\dfrac{5+2x}{x(x-3)}$

Work Step by Step

Factoring the given expression, $ \dfrac{5}{x^2-3x}+\dfrac{4}{2x-6} ,$ results to \begin{array}{l}\require{cancel} \dfrac{5}{x(x-3)}+\dfrac{4}{2(x-3)} .\end{array} Using the $LCD= 2x(x-3) $, the expression above simplifies to \begin{array}{l} \dfrac{2(5)+x(4)}{2x(x-3)} \\\\= \dfrac{10+4x}{2x(x-3)} \\\\= \dfrac{2(5+2x)}{2x(x-3)} \\\\= \dfrac{\cancel{2}(5+2x)}{\cancel{2}x(x-3)} \\\\= \dfrac{5+2x}{x(x-3)} .\end{array}
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