Answer
$x=-1$ or $x=-6$.
Work Step by Step
LCD$=x$, thus multiplying both sides by the LCD: $x(x+\frac{6}{x})=x(-7)\\x^2+7x+6=0\\x^2+x+6x+6=0\\x(x+1)+6(x+1)=0\\(x+1)(x+6)=0$
Thus $x=-1$ or $x=-6$.
Intermediate Algebra for College Students (7th Edition)
by Blitzer, Robert F.
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: 20
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