Functions Modeling Change: A Preparation for Calculus, 5th Edition

by Connally, Eric; Hughes-Hallett, Deborah; Gleason, Andrew M.; Cheifetz, Phil C.

Published by Wiley

ISBN 10: 1118583191

ISBN 13: 978-1-11858-319-7

Chapter 10 - Compositions, Inverses, and Combinations of Functions - Review Exercises and Problems for Chapter Ten - Page 427: 85

Answer

$$x=\frac{3+\sqrt{17}}{4},\:x=\frac{3-\sqrt{17}}{4}$$

Work Step by Step

Using the rules of algebra, we obtain: $$2x-3=\frac{\left(2x-1\right)}{2x+1} \\ 2x\left(2x+1\right)-3\left(2x+1\right)=\frac{2x-1}{2x+1}\left(2x+1\right) \\ x=\frac{3+\sqrt{17}}{4},\:x=\frac{3-\sqrt{17}}{4}$$

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