Calculus with Applications (10th Edition)

Published by Pearson
ISBN 10: 0321749006
ISBN 13: 978-0-32174-900-0

Chapter R - Algebra Reference - R.4 Equations - R.4 Exercises - Page R-16: 29


The solution is $x=-\dfrac{59}{6}$

Work Step by Step

$\dfrac{4}{x-3}-\dfrac{8}{2x+5}+\dfrac{3}{x-3}=0$ Multiply the whole equation by $(x-3)(2x+5)$: $(x-3)(2x+5)\Big(\dfrac{4}{x-3}-\dfrac{8}{2x+5}+\dfrac{3}{x-3}=0\Big)$ $4(2x+5)-8(x-3)+3(2x+5)=0$ $8x+20-8x+24+6x+15=0$ Simplify by combining like terms: $6x+59=0$ Take $59$ to the right side: $6x=-59$ Take $6$ to divide the right side: $x=-\dfrac{59}{6}$
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