Answer
$-\frac{2x+h}{x^{2}(x+h)^{2}}$
Work Step by Step
$\dfrac{\frac{1}{(x+h)^{2}}-\frac{1}{x^{2}}}{h}$
Evaluate the substraction of fractions in the numerator:
$\dfrac{\frac{1}{(x+h)^{2}}-\frac{1}{x^{2}}}{h}=\dfrac{\frac{x^{2}-(x+h)^{2}}{x^{2}(x+h)^{2}}}{h}=...$
Evaluate the division:
$...=\dfrac{x^{2}-(x+h)^{2}}{x^{2}h(x+h)^{2}}=...$
Factor the difference of squares in the numerator:
$...=\dfrac{[x-(x+h)][x+(x+h)]}{x^{2}h(x+h)^{2}}=...$
Simplify:
$...=\dfrac{(-h)(2x+h)}{x^{2}h(x+h)^{2}}=-\dfrac{2x+h}{x^{2}(x+h)^{2}}$
