Algebra: A Combined Approach (4th Edition)

Published by Pearson
ISBN 10: 0321726391
ISBN 13: 978-0-32172-639-1

Chapter 7 - Section 7.5 - Solving Equations Containing Rational Expressions - Exercise Set: 27

Answer

-4 and 3

Work Step by Step

$\frac{a}{a-6}$=$\frac{-2}{a-1}$ (a-6)(a-1)[$\frac{a}{a-6}$]=(a-6)(a-1)$\frac{-2}{a-1}$ (a-1)a=-2(a-6) $a^{2}$-a=-2a+12 $a^{2}$-a+2a-12=0 $a^{2}$+a-12=0 $a^{2}$-3a+4a-12=0 a(a-3)+4(a-3)=0 (a+4)(a-3)=0 a+4=0 or a-3=0 a=-4 or a=3 The solutions are -4 and 3 Check Let a=3 $\frac{a}{a-6}$=$\frac{-2}{a-1}$ $\frac{3}{3-6}$=$\frac{-2}{3-1}$ $\frac{3}{-3}$=$\frac{-2}{2}$ -1=-1 Let a=-4 $\frac{a}{a-6}$=$\frac{-2}{a-1}$ $\frac{-4}{-4-6}$=$\frac{-2}{-4-1}$ $\frac{-4}{-10}$=$\frac{-2}{-5}$ $\frac{-2}{-5}$=$\frac{-2}{-5}$
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