Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 1 - Functions and Limits - 1.1 Four Ways to Represent a Function - 1.1 Exercises - Page 21: 30


$\frac{f(x)-f(1)}{x-1} =\frac{-1}{(x+1)}$

Work Step by Step

$f(x) = \frac{x+3}{x+1}$ (*) $f(1) = \frac{1+3}{1+1}=\frac{4}{2}=2$ $\frac{f(x)-f(1)}{x-1} = \frac{\frac{x+3}{x+1}-2}{x-1}=\frac{\frac{x+3-2(x+1)}{x+1}}{x-1}=\frac{\frac{x+3-2x-2}{x+1}}{x-1}=\frac{x+3-2x-2}{(x+1)(x-1)}=\frac{-x+1}{(x+1)(x-1)}=\frac{-(x-1)}{(x+1)(x-1)}=\frac{-1}{(x+1)}$
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