Question

Evaluate the difference quotient for the given function.
f(x) = (x+5)/(x + 2)

(f(x) − f(1))/(x − 1)

Answer 1

ick!

Answer 2

lets make life easy and compute
\[f(1)=\frac{1+5}{1+2}=\frac{6}{3}=2\] forst

Answer 3

so you have
\[\frac{f(x)-2}{x-1}\] as a start

Answer 4

i should just quit. i keep putting x + 1 when it is x + 2
this time for real
\[f(x)-2=\frac{x+5}{x+2}-2=\frac{x+5-2(x+2)}{x+2}\]
\[=\frac{x+5-2x-4}{x+2}=\frac{1-x}{x+2}\] there now it is right!

Answer 5

now divide by
\[x-1\] and get
\[\frac{1-x}{(x-1)(x+2)}=\frac{-1}{x+2}\]

Answer 6

because
\[\frac{1-x}{x-1}=-1\]

Answer 7

sorry i messed up twice with those stupid typos. it is right now

Answer 8

thank you for the step-by-step analysis!