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: 29

Answer

The solutions are $x=\dfrac{1}{9}$ and $x=-\dfrac{5}{2}$

Work Step by Step

$\dfrac{5}{x^{2}}-\dfrac{43}{x}=18$ Multiply the whole equation by $x^{2}$: $x^{2}\Big(\dfrac{5}{x^{2}}-\dfrac{43}{x}=18\Big)$ $5-43x=18x^{2}$ Take all terms to the right side of the equation and rearrange: $0=18x^{2}+43x-5$ $18x^{2}+43x-5=0$ Solve by factoring: $(2x+5)(9x-1)=0$ Set both factors equal to $0$ and solve each individual equation for $x$: $2x+5=0$ $2x=-5$ $x=-\dfrac{5}{2}$ $9x-1=0$ $9x=1$ $x=\dfrac{1}{9}$ The solutions are $x=\dfrac{1}{9}$ and $x=-\dfrac{5}{2}$
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