Finite Math and Applied Calculus (6th Edition)

Published by Brooks Cole
ISBN 10: 1133607705
ISBN 13: 978-1-13360-770-0

Chapter 0 - Section 0.4 - Rational Expressions - Exercises - Page 23: 11

Answer

$\frac{x^{2}+2x+1}{x^{4}+8x^{3}+24x^{2}+32x+16}$

Work Step by Step

$\frac{(x+1)^{2}(x+2)^{3}-(x+1)^{3}(x+2)^{2}}{(x+2)^{6}}=\frac{(x+2)^{2}(x+1)^{2}(x+2-(x+1))}{(x+2)^{6}}=\frac{(x+1)^{2}}{(x+2)^{4}}=\frac{x^{2}+2x+1}{(x^{2}+4x+4)(x^{2}+4x+4)}=\frac{x^{2}+2x+1}{x^{4}+8x^{3}+24x^{2}+32x+16}$
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