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: 30

Answer

$\dfrac{x+1}{2x^{2}+5x+3}\div\dfrac{20x+100}{2x+3}=\dfrac{1}{20(x+5)}$

Work Step by Step

$\dfrac{x+1}{2x^{2}+5x+3}\div\dfrac{20x+100}{2x+3}$ Factor the denominator of the first fraction and take out common factor $20$ from the numerator of the second fraction: $\dfrac{x+1}{2x^{2}+5x+3}\div\dfrac{20x+100}{2x+3}=\dfrac{x+1}{(2x+3)(x+1)}\div\dfrac{20(x+5)}{2x+3}$ Evaluate the division of the two rational expressions and simplify by removing repeated factors in the numerator and the denominator: $...=\dfrac{(2x+3)(x+1)}{20(2x+3)(x+1)(x+5)}=\dfrac{1}{20(x+5)}$
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