Algebra: A Combined Approach (4th Edition)

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

Chapter 7 - Section 7.3 - Adding and Subtracting Rational Expressions with the Same Denominator and Least Common Denominator - Exercise Set: 55

Answer

$\dfrac{x^{3}+7x^{2}}{3x^{3}-x^{2}}\div\dfrac{5x^{2}+36x+7}{9x^{2}-1}=\dfrac{3x+1}{5x+1}$

Work Step by Step

$\dfrac{x^{3}+7x^{2}}{3x^{3}-x^{2}}\div\dfrac{5x^{2}+36x+7}{9x^{2}-1}$ Factor both rational expressions completely: $\dfrac{x^{3}+7x^{2}}{3x^{3}-x^{2}}\div\dfrac{5x^{2}+36x+7}{9x^{2}-1}=\dfrac{x^{2}(x+7)}{x^{2}(3x-1)}\div\dfrac{(x+7)(5x+1)}{(3x-1)(3x+1)}$ Evaluate the division and simplify by removing the factors that appear both in the numerator and the denominator of the resulting expressions: $...=\dfrac{x^{2}(x+7)(3x-1)(3x+1)}{x^{2}(3x-1)(x+7)(5x+1)}=\dfrac{3x+1}{5x+1}$
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