Algebra: A Combined Approach (4th Edition)

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

Chapter 7 - Section 7.2 - Multiplying and Dividing Rational Expressions - Exercise Set: 29

Answer

$\dfrac{x^{2}+7x+10}{x-1}\div\dfrac{x^{2}+2x-15}{x-1}=\dfrac{x+2}{x-3}$

Work Step by Step

$\dfrac{x^{2}+7x+10}{x-1}\div\dfrac{x^{2}+2x-15}{x-1}$ Factor the numerators of both fractions: $\dfrac{(x+5)(x+2)}{x-1}\div\dfrac{(x+5)(x-3)}{x-1}=...$ Evaluate the division of the two rational expressions and simplify by removing repeated factors in the numerator and the denominator of the resulting expression: $...=\dfrac{(x-1)(x+5)(x+2)}{(x-1)(x+5)(x-3)}=\dfrac{x+2}{x-3}$
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