College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter 1 - Section 1.2 - Quadratic Equations - 1.2 Assess Your Understanding - Page 102: 65


$\displaystyle x=\frac{9\pm\sqrt{73}}{2}$

Work Step by Step

$\displaystyle \frac{3x}{x-2}+\frac{1}{x}=4$ We multiply through by $x(x-2)$: $\displaystyle x(x-2)(\frac{3x}{x-2}+\frac{1}{x})=x(x-2)*4$ $3x*x+(x-2)=4x^{2}-8x$ $3x^{2}+x-2=4x^{2}-8x$ $x^{2}-9x+2=0$ We solve using the quadratic formula ($a=1,\ b=-9,\ c=2$): $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$ $\displaystyle x=\frac{-(-9)\pm\sqrt{(-9)^{2}-4*1*2}}{2*1}$ $\displaystyle x=\frac{9\pm\sqrt{81-8}}{2}$ $\displaystyle x=\frac{9\pm\sqrt{73}}{2}$
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