Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter 1 - Equations and Inequalities - 1.6 Other Types of Equations and Applications - 1.6 Exercises: 36

Answer

The solutions are $x=-1$ and $x=\dfrac{2}{3}$

Work Step by Step

$\dfrac{3x^{2}}{x-1}+2=\dfrac{x}{x-1}$ Multiply the whole equation by $x-1$: $(x-1)\Big(\dfrac{3x^{2}}{x-1}+2=\dfrac{x}{x-1}\Big)$ $3x^{2}+2(x-1)=x$ Evaluate the indicated operations: $3x^{2}+2x-2=x$ Take $x$ to the left side and simplify: $3x^{2}+2x-x-2=0$ $3x^{2}+x-2=0$ Solve by factoring: $(x+1)(3x-2)=0$ Set both factors equal to $0$ and solve each individual equation for $x$: $x+1=0$ $x=-1$ $3x-2=0$ $3x=2$ $x=\dfrac{2}{3}$ The solutions are $x=-1$ and $x=\dfrac{2}{3}$
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