Answer
$\frac{-4x-2h}{((x+h)^2+16)(x^2+16)}$
Work Step by Step
Step 1. Perform operations to the numerator:
$\frac{2}{(x+h)^2+16}-\frac{2}{x^2+16}=2\cdot\frac{x^2+16-(x+h)^2-16}{((x+h)^2+16)(x^2+16)}=\frac{-4xh-2h^2}{((x+h)^2+16)(x^2+16)}$
Step 2. Use the above results in the original expression, we have:
$\frac{\frac{2}{(x+h)^2+16}-\frac{2}{x^2+16}}{h}=\frac{\frac{-4xh-2h^2}{((x+h)^2+16)(x^2+16)}}{h}=\frac{-4x-2h}{((x+h)^2+16)(x^2+16)}$
