Algebra: A Combined Approach (4th Edition)

Published by Pearson
ISBN 10: 0321726391
ISBN 13: 978-0-32172-639-1

Chapter 7 - Section 7.5 - Solving Equations Containing Rational Expressions - Exercise Set: 28

Answer

The solutions are 1 and 10

Work Step by Step

$\frac{5}{x-6}$=$\frac{x}{x-2}$ (x-6)(x-2)$\frac{5}{x-6}$=(x-6)(x-2)$\frac{x}{x-2}$ $\frac{5}{x-6}$=$\frac{x}{x-2}$ (x-2)5=(x-6)x 5x-10=$x^{2}$-6x 0=$x^{2}$-6x-5x+10 0=$x^{2}$-11x+10 0=$x^{2}$-x-10x+10 0=x(x-1)-10(x-1) 0=(x-10)(x-1) x-10=0 or x-1=0 x=10 or x=1 The solutions are 1 and 10 Check Let x=1 $\frac{5}{x-6}$=$\frac{x}{x-2}$ $\frac{5}{1-6}$=$\frac{1}{1-2}$ $\frac{5}{-5}$=$\frac{1}{-1}$ -1=-1 Let x=10 $\frac{5}{x-6}$=$\frac{x}{x-2}$ $\frac{5}{10-6}$=$\frac{10}{10-2}$ $\frac{5}{4}$=$\frac{10}{8}$ $\frac{5}{4}$=$\frac{5}{4}$
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