College Algebra 7th Edition

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

Chapter 1, Equations and Graphs - Chapter 1 Review - Exercises: 57

Answer

$\frac{3\pm\sqrt{6}}{3}$

Work Step by Step

$ \frac{1}{x}+\frac{2}{x-1}=3$ We multiply through by $(x-1)x$: $(x-1)+2(x)=3(x)(x-1)$ $x-1+2x=3x^{2}-3x$ $0=3x^{2}-6x+1$ Next we use the quadratic formula ($a=3, b=-6, c=1$): $x= \frac{-b\pm\sqrt{b^{2}-4ac}}{2a}=\frac{--6\pm\sqrt{(-6)^{2}-4*3*1}}{2*3}=\frac{6\pm\sqrt{36-12}}{6}=\frac{6\pm\sqrt{24}}{6}=\frac{6\pm 2\sqrt{6}}{6}=\frac{3\pm\sqrt{6}}{3}$
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