What is the average rate of change between x and x + h for the function $\displaystyle f(x)=(2x+4)/x$ . Show your simplification.
$\displaystyle f(x)=\dfrac{2x+4}{x}$
Find f(x + h):
$\displaystyle f(x)=\dfrac{2(x+h)+4}{x+h} = \ldots$
Plug f(x + h) and f(x) into
$\displaystyle \dfrac{f(x + h) - f(x)}{h}$
and simplify.
$\displaystyle \dfrac{f(x + h) - f(h)}{h}$ is incorrect. It should be
$\displaystyle \dfrac{f(x + h) - f(x)}{h}.$ That's the slope of the secant line, which also happens to be equal to the average rate of change.
[EDIT] Typo fixed.