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: 32


$\displaystyle \frac{5\pm 3\sqrt{5}}{2}=\frac{5}{2}\pm\frac{3\sqrt{5}}{2}$

Work Step by Step

$\displaystyle \frac{x}{x+3}=\frac{2}{x-3}-\frac{1}{x^{2}-9}$ We multiply through by $(x-3)(x+3)$: $x(x-3)=2(x+3)-1$ And distribute: $x^{2}-3x=2x+6-1$ $x^{2}-3x-2x-6+1=0$ $x^{2}-5x-5=0$ Now we use the quadratic formula $(a=1, b=-5, c=-5)$: $x=\displaystyle \frac{-(-5)\pm\sqrt{(-5)^{2}-4*1*-5}}{2}=\frac{5\pm 3\sqrt{5}}{2}=\frac{5}{2}\pm\frac{3\sqrt{5}}{2}$
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