Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 1 - Section 1.4 - Rational Expressions - 1.4 Exercises: 76

Answer

$\dfrac{(x+h)^{3}-7(x+h)-(x^{3}-7x)}{h}=3x^{2}+3xh+h^{2}-7$

Work Step by Step

$\dfrac{(x+h)^{3}-7(x+h)-(x^{3}-7x)}{h}$ Evaluate $(x+h)^{3}$: $\dfrac{(x+h)^{3}-7(x+h)-(x^{3}-7x)}{h}=...$ $...=\dfrac{(x^{3}+3x^{2}h+3xh^{2}+h^{3})-7(x+h)-(x^{3}-7x)}{h}=...$ Simplify the numerator: $...=\dfrac{(x^{3}+3x^{2}h+3xh^{2}+h^{3})-7x-7h-x^{3}+7x}{h}=...$ $...=\dfrac{x^{3}+3x^{2}h+3xh^{2}+h^{3}-7x-7h-x^{3}+7x}{h}=...$ $...=\dfrac{3x^{2}h+3xh^{2}+h^{3}-7h}{h}=...$ Take out common factor $h$ from the numerator and simplify: $...=\dfrac{h(3x^{2}+3xh+h^{2}-7)}{h}=3x^{2}+3xh+h^{2}-7$
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