Intermediate Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-894-7
ISBN 13: 978-0-13417-894-3

Chapter 6 - Section 6.6 - Rational Equations - Exercise Set - Page 462: 10

Answer

Solution set = $\{38\}$.

Work Step by Step

First, we exclude those values of x that yield a zero in any of the denominators. $x\not\in\{-4,-10\}\qquad (*)$ Multiply the equation with the LCD=$(x+10)(x+4)$ $(x+2)(x+4)=(x-3)(x+10)\qquad$ ... simplify (distribute) $x^{2}+4x+2x+8=x^{2}+10x-3x-30$ $ x^{2}+6x+8=x^{2}+7x-30\qquad$ ... add $-8-x^{2}-7x$ $6x-7x=-30-8$ $-x=-38$ $ x=38\qquad$ ...Checking (*), this is a valid solution Solution set = $\{38\}$.
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