Introductory Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-805-X
ISBN 13: 978-0-13417-805-9

Chapter 7 - Section 7.1 - Rational Expressions and Their Simplification - Exercise Set - Page 493: 105


False. Change to: For $x=\displaystyle \frac{1}{3},\quad\frac{3x+7}{3x+10}=\frac{8}{11}$

Work Step by Step

If this were true, it would be true for any x, provided it doesn't yield 0 in the denominator. Try x=0: $LHS=\displaystyle \frac{0+7}{0+10}=\frac{7}{10}\neq\frac{8}{11}$ so, the statement is false. It is true only when $x=\displaystyle \frac{1}{3},$ $LHS=\displaystyle \frac{3\cdot\frac{1}{3}+7}{3\cdot\frac{1}{3}+10}=\frac{1+7}{1+10}=\frac{8}{11}$
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