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 463: 41


Solution set: $\{2\}$

Work Step by Step

Factor the denominators $x^{2}-x=x(x-1)$ $x^{2}-1=(x-1)(x+1)$ LCD = $x(x-1)(x+1)$ $\displaystyle \frac{x+2}{x(x-1)}-\frac{6}{(x-1)(x+1)}=0$ Exclude solutions which yield 0 in denominators: $x\not\in\{0,-1,1\}\qquad (*)$ Multiply with the LCD, $x(x-1)(x+1)$ $(x+2)(x+1)-6\cdot x=0$ $x^{2}+3x+2-6x=0$ $x^{2}-3x+2=0$ ... factors of 2 whose sum is -3 ... are -1 and -2 $(x-1)(x-2)=0\qquad$ ... apply the zero product principle $ x=1\qquad$ ... is excluded, see (*). $x=2$ Solution set: $\{2\}$
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