Answer
$\dfrac{\dfrac{1}{\sqrt{x+h}}-\dfrac{1}{\sqrt{x}}}{h}=\dfrac{\sqrt{x}-\sqrt{x+h}}{h\sqrt{x^{2}+xh}}$
Work Step by Step
$\dfrac{\dfrac{1}{\sqrt{x+h}}-\dfrac{1}{\sqrt{x}}}{h}$
Evaluate the subtraction in the numerator:
$\dfrac{\dfrac{1}{\sqrt{x+h}}-\dfrac{1}{\sqrt{x}}}{h}=\dfrac{\dfrac{\sqrt{x}-\sqrt{x+h}}{(\sqrt{x})(\sqrt{x+h})}}{h}=...$
Evaluate the division:
$...=\dfrac{\sqrt{x}-\sqrt{x+h}}{h(\sqrt{x})(\sqrt{x+h})}=...$
Evaluate the product in the denominator:
$...=\dfrac{\sqrt{x}-\sqrt{x+h}}{h\sqrt{x^{2}+xh}}$
