Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter P - Section P.7 - Equations - Exercise Set - Page 106: 17


$a.\quad x\neq 1$ $ b.\quad$ Solution set = $\{3\}$

Work Step by Step

$a.$ The denominators in the equation must not be zero: $x-1\Rightarrow x\neq 1 \qquad(*)$ $b.$ Multiply both sides with the LCD,$\quad(x-1)$ $(x-1)\left[ \displaystyle \frac{1}{x-1}+5 \right] = (x-1)\left[ \dfrac{11}{x-1} \right]\quad$ ... distribute and simplify $ 1+5(x-1)=11\quad$ ... distribute and simplify $1+5x-5=11$ $ 5x-4=11\quad$ ... add $4$ to both sides $5x=15$ $ x=3\quad$ ... satisfies (*), a valid solution. Solution set = $\{3\}$
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