College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter 3 - Section 3.1 - Functions - 3.1 Assess Your Understanding - Page 212: 88


$- \displaystyle \frac{20}{(x+h-4)(x-4)}$

Work Step by Step

$f(x)=\displaystyle \frac{5x}{x-4}$ $\displaystyle \frac{f(x+h)-f(x)}{h}=\frac{1}{h}\cdot (\frac{5(x+h)}{x+h-4}-\frac{5x}{x-4})$ ... LCD=$(x+h-4)(x-4)$ $=\displaystyle \frac{1}{h}\cdot\frac{5(x+h)(x-4)-5x(x-4+h)}{(x+h-4)(x-4)}$ $=\displaystyle \frac{1}{h}\cdot \frac{5x^{2}-20x+5hx-20h-5x^{2}+20x-5xh}{(x+h-4)(x-4)}$ $=\displaystyle \frac{1}{h}\cdot \frac{-20h}{(x+h-4)(x-4)}$ ... h cancels $=- \displaystyle \frac{20}{(x+h-4)(x-4)}$
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