Answer
$2x+h$
Work Step by Step
RECALL:
$\\\\$The difference quotient of a function $f$ is given by the formula $\dfrac{f(x+h)-f(x)}{h}$ where $h \ne0$.
Use the difference quotient formula above to obtain:
$\dfrac{f(x+h)-f(x)}{h}\\
=\dfrac{[(x+h)^2-4]-(x^2-4)}{h}\\
=\dfrac{(x^2+2xh+h^2-4)-(x^2-4)}{h}\\
=\dfrac{x^2+2xh+h^2-4-x^2+4}{h}\\
=\dfrac{2xh+h^2}{h}\\
=\dfrac{h(2x+h)}{h}\\
=2x+h$
