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: 35

Answer

The solutions are $x=-2$ and $x=\dfrac{5}{4}$

Work Step by Step

$\dfrac{2x}{x-2}=5+\dfrac{4x^{2}}{x-2}$ Multiply the whole equation by $x-2$: $(x-2)\Big(\dfrac{2x}{x-2}=5+\dfrac{4x^{2}}{x-2}\Big)$ $2x=5(x-2)+4x^{2}$ Evaluate the indicated operations: $2x=5x-10+4x^{2}$ Take $2x$ to the right side and simplify: $0=5x-10+4x^{2}-2x$ $0=4x^{2}+3x-10$ Rearrange: $4x^{2}+3x-10=0$ $(x+2)(4x-5)=0$ Set both factors equal to $0$ and solve each individual equation for $x$: $x+2=0$ $x=-2$ $4x-5=0$ $4x=5$ $x=\dfrac{5}{4}$ The solutions are $x=-2$ and $x=\dfrac{5}{4}$
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