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: 36

Answer

$ x=\dfrac{7+\sqrt{57}}{4}$ or $x=\dfrac{7-\sqrt{57}}{4}$

Work Step by Step

$\dfrac{3+\frac{1}{x}}{2-\frac{4}{x}}=x$ Simplify $\Rightarrow \dfrac{\frac{3x+1}{x}}{\frac{2x-4}{x}}=x$ Simplify $\Rightarrow \dfrac{3x+1}{2x-4}=x$ cross-multiply: $\Rightarrow 3x+1=x(2x-4)$ $\Rightarrow 3x+1=2x^2-4x$ $\Rightarrow 2x^2-7x-1=0$ Use the quadratic formula, where $a=2, b=-7$ and $c=-1$ $x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}=\dfrac{-(-7)\pm\sqrt{(-7)^2-4(2)(-1)}}{2(2)}$ $\Rightarrow x=\dfrac{7\pm\sqrt{49+8}}{4}=\dfrac{7\pm\sqrt{57}}{4}$ $\Rightarrow x=\dfrac{7+\sqrt{57}}{4}$ or $x=\dfrac{7-\sqrt{57}}{4}$
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