College Algebra (6th Edition)

Published by Pearson
ISBN 10: 0-32178-228-3
ISBN 13: 978-0-32178-228-1

Chapter 1 - Equations and Inequalities - Exercise Set 1.2: 59

Answer

$x=-1$

Work Step by Step

$y=\dfrac{x+6}{3x-12}-\dfrac{5}{x-4}-\dfrac{2}{3}$ Set $y$ equal to $0$: $\dfrac{x+6}{3x-12}-\dfrac{5}{x-4}-\dfrac{2}{3}=0$ Factor the denominator of the first fraction: $\dfrac{x+6}{3(x-4)}-\dfrac{5}{x-4}-\dfrac{2}{3}=0$ Multiply the whole equation by $3(x-4)$: $3(x-4)\Big[\dfrac{x+6}{3(x-4)}-\dfrac{5}{x-4}-\dfrac{2}{3}=0\Big]$ $(x+6)-(5)(3)-2(x-4)=0$ $x+6-15-2x+8=0$ Take all terms without $x$ to the right side, simplify and solve for $x$: $x-2x=-8-6+15$ $-x=1$ $x=-1$
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