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: 18

Answer

The solution is $x=\dfrac{3}{5}$

Work Step by Step

$\dfrac{4x+3}{4}-\dfrac{2x}{x+1}=x$ Multiply the whole equation by $4(x+1)$: $4(x+1)\Big(\dfrac{4x+3}{4}-\dfrac{2x}{x+1}=x\Big)$ $(x+1)(4x+3)-2x(4)=4x(x+1)$ Evaluate the indicated operations and simplify the equation: $4x^{2}+7x+3-8x=4x^{2}+4x$ $4x^{2}+7x+3-8x-4x^{2}-4x=0$ $-5x+3=0$ Solve for $x$: $-5x=-3$ $x=\dfrac{3}{5}$
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