Answer
$3x^{2}+3xh+h^{2}-7$
Work Step by Step
We distribute everything, simplify, factor, and simplify again:
$\displaystyle \frac{(x+h)^{3}-7(x+h)-(x^{3}-7x)}{h}=\frac{x^{3}+3x^{2}h+3xh^{2}+h^{3}-7x-7h-x^{3}+7x}{h}=\frac{3x^{2}h+3xh^{2}+h^{3}-7h}{h}
=\frac{h(3x^{2}+3xh+h^{2}-7)}{h}=3x^{2}+3xh+h^{2}-7$
