College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter 1, Equations and Graphs - Section 1.6 - Solving Other Types of Equations - 1.6 Exercises - Page 138: 33


$\displaystyle x=-\frac{7}{3}$ or $x=-4$

Work Step by Step

$\displaystyle \frac{x}{2x+7}-\frac{x+1}{x+3}=1$ We multiply through by $(2x+7)(x+3)$: $x(x+3)-(x+1)(2x+7)=(2x+7)(x+3)$ And distribute: $x^{2}+3x-2x^{2}-9x-7=2x^{2}+13x+21$ And simplify: $x^{2}+3x-2x^{2}-9x-7-2x^{2}-13x-21=0$ $3x^{2}+19x+28=0$ And factor: $(3x+7)(x+4)=0$ $3x+7=0$ or $x+4=0$ $x=-\frac{7}{3}$ or $x=-4$
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