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: 16

Answer

$\dfrac{x^{2}+9x+20}{x^{2}-15x+44}\cdot\dfrac{x^{2}-11x+28}{x^{2}+12x+35}=\dfrac{(x+4)(x-7)}{(x-11)(x+7)}$

Work Step by Step

$\dfrac{x^{2}+9x+20}{x^{2}-15x+44}\cdot\dfrac{x^{2}-11x+28}{x^{2}+12x+35}$ Factor both rational expression completely: $\dfrac{(x+5)(x+4)}{(x-4)(x-11)}\cdot\dfrac{(x-4)(x-7)}{(x+7)(x+5)}=...$ Multiply the two expressions and simplify by removing repeated factors in the numerator and the denominator: $...=\dfrac{(x+5)(x+4)(x-4)(x-7)}{(x-4)(x-11)(x+7)(x+5)}=\dfrac{(x+4)(x-7)}{(x-11)(x+7)}$
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