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: 19


$a.\quad x\neq-1$ $ b.\quad$ Solution set = $\emptyset$

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,$\quad(x+1)$ $(x+1) \displaystyle \left[ \frac{8x}{x+1} \right] = (x+1) \left[ 4-\frac{8}{x+1} \right]\quad$ ... distribute and simplify $ 8x=4(x+1)-8\quad$ ... distribute and simplify $8x=4x+4-8$ $ 8x=4x-4\quad$ ... add $-4x$ to both sides $4x=-4$ $ x=-1 \quad$ ... clashes with (*), not a valid solution. Solution set = $\emptyset$
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