College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter P, Prerequisites - Section P.7 - Rational Expressions - P.7 Exercises: 76

Answer

$3x^{2}+3xh+h^{2}-7$

Work Step by Step

We distribute everything, simplify, factor, and simplify again: $\displaystyle \frac{(x+h)^{3}-7(x+h)-(x^{3}-7x)}{h}=\frac{x^{3}+3x^{2}h+3xh^{2}+h^{3}-7x-7h-x^{3}+7x}{h}=\frac{3x^{2}h+3xh^{2}+h^{3}-7h}{h} =\frac{h(3x^{2}+3xh+h^{2}-7)}{h}=3x^{2}+3xh+h^{2}-7$
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