Answer
$6x+3h$
Work Step by Step
$f(x)=3x^{2}+2$
$\displaystyle \frac{f(x+h)-f(x)}{h}=\frac{3(x+h)^{2}+2-(3x^{2}+2)}{h}$
... expand the square, $(a+b)^{2}=a^{2}+2ab+b^{2}$
$=\displaystyle \frac{3x^{2}+6xh+3h^{2}+2-3x^{2}-2}{h}$
... simplify: the $x^{2}$ terms, and the constants cancel,
$=\displaystyle \frac{6xh+3h^{2}}{h}$
...factor out h
$=\displaystyle \frac{h(6x+3h)}{h}$
... h cancels
$=6x+3h$
