Question

Consider the function below.
f(x)=(x+4)/(x+2)
Evaluate the difference quotient for the given function. Simplify your answer.
(f(x) - f(2))/(x-2) ** Please explain how you got your answer so I can understand the problem. Thanks!

Answer 1

\[\frac{ f(x)-f(2) }{ x-2 }=\frac{ \frac{ x+4 }{x+2 }-\frac{ 6 }{ 4} }{ x-2 }\]
\[\frac{ \frac{ x+4 }{x+2 }-\frac{ 3 }{ 2} }{ x-2 }=\frac{ \frac{ 2(x+4 )-3(x+2)}{2(x+2) } }{ x-2 }\]
\[\frac{ \frac{ 2x+8-3x-6}{2(x+2) } }{ x-2 }=\frac{ \frac{ -x+2}{2(x+2) } }{ x-2 }=\]
\[\frac{ \frac{ -(x-2)}{2(x+2) } }{ x-2 }=\frac{ \frac{ -1}{2(x+2) } }{1 }=\frac{ -1 }{ 2(x+2) }\]

Answer 2

THANKS