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: 32

Answer

$x=\{2,10\}$

Work Step by Step

Multiplying both sides by the $LCD= 4x ,$ then the given equation, $ \dfrac{x}{4}+\dfrac{5}{x}=3 ,$ simplifies to \begin{array}{l}\require{cancel} x(x)+4(5)=4x(3) \\\\ x^2+20=12x \\\\ x^2-12x+20=0 \\\\ (x-10)(x-2)=0 \\\\ x=\{2,10\} .\end{array} Upon checking, both solutions satisfy the original equation. Hence, there is $ x=\{2,10\} .$
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