Answer
$\dfrac{(x+h)^{3}-7(x+h)-(x^{3}-7x)}{h}=3x^{2}+3xh+h^{2}-7$
Work Step by Step
$\dfrac{(x+h)^{3}-7(x+h)-(x^{3}-7x)}{h}$
Evaluate $(x+h)^{3}$:
$\dfrac{(x+h)^{3}-7(x+h)-(x^{3}-7x)}{h}=...$
$...=\dfrac{(x^{3}+3x^{2}h+3xh^{2}+h^{3})-7(x+h)-(x^{3}-7x)}{h}=...$
Simplify the numerator:
$...=\dfrac{(x^{3}+3x^{2}h+3xh^{2}+h^{3})-7x-7h-x^{3}+7x}{h}=...$
$...=\dfrac{x^{3}+3x^{2}h+3xh^{2}+h^{3}-7x-7h-x^{3}+7x}{h}=...$
$...=\dfrac{3x^{2}h+3xh^{2}+h^{3}-7h}{h}=...$
Take out common factor $h$ from the numerator and simplify:
$...=\dfrac{h(3x^{2}+3xh+h^{2}-7)}{h}=3x^{2}+3xh+h^{2}-7$
