Intermediate Algebra (6th Edition)

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

Chapter 6 - Test - Page 406: 23



Work Step by Step

The factored form of the given equation, $ \dfrac{3}{x+2}-\dfrac{1}{5x}=\dfrac{2}{5x^2+10x} ,$ is \begin{array}{l}\require{cancel} \dfrac{3}{x+2}-\dfrac{1}{5x}=\dfrac{2}{5x(x+2)} .\end{array} Multiplying both sides by the $LCD= 5x(x+2) ,$ then the given equation simplifies to \begin{array}{l}\require{cancel} 5x(3)-(x+2)(1)=1(2) \\\\ 15x-x-2=2 \\\\ 15x-x=2+2 \\\\ 14x=4 \\\\ x=\dfrac{4}{14} \\\\ x=\dfrac{\cancel{2}\cdot2}{\cancel{2}\cdot7} \\\\ x=\dfrac{2}{7} .\end{array}
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