Answer
$\frac{-2x-h}{((x+h)^2+9)(x^2+9)}$
Work Step by Step
Step 1. Perform operations to the numerator:
$\frac{1}{(x+h)^2+9}-\frac{1}{x^2+9}=\frac{x^2+9-(x+h)^2-9}{((x+h)^2+9)(x^2+9)}=\frac{-2xh-h^2}{((x+h)^2+9)(x^2+9)}$
Step 2. Use the above results in the original expression, we have:
$\frac{\frac{1}{(x+h)^2+9}-\frac{1}{x^2+9}}{h}=\frac{\frac{-2xh-h^2}{((x+h)^2+9)(x^2+9)}}{h}=\frac{-2x-h}{((x+h)^2+9)(x^2+9)}$
