Intermediate Algebra (6th Edition)

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

Chapter 6 - Section 6.5 - Solving Equations Containing Rational Expressions - Exercise Set - Page 378: 20


no solution

Work Step by Step

The factored form of the given equation, $ \dfrac{2}{x^2-4}=\dfrac{1}{2x-4} ,$ is \begin{array}{l}\require{cancel} \dfrac{2}{(x+2)(x-2)}=\dfrac{1}{2(x-2)} .\end{array} Multiplying both sides by the $LCD= 2(x+2)(x-2) ,$ then \begin{array}{l}\require{cancel} 2(2)=(x+2)(1) \\\\ 4=x+2 \\\\ -x=2-4 \\\\ -x=-2 \\\\ x=2 .\end{array} Upon checking, $x=2$ does not satisfy the original equation. Hence, there is $\text{ no solution .}$
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