Answer
The solution is
$$\frac{f(x+h)-f(x)}{h}=\frac{-2}{(\sqrt{1-2x-2h}+\sqrt{1-2x})}$$
Work Step by Step
The expression becomes
$$\frac{f(x+h)-f(x)}{h}=\frac{\sqrt{1-2(x+h)}-\sqrt{1-2x}}{h}=\frac{\sqrt{1-2x-2h}-\sqrt{1-2x}}{h}=\frac{\sqrt{1-2x-2h}-\sqrt{1-2x}}{h}\cdot\frac{\sqrt{1-2x-2h}+\sqrt{1-2x}}{\sqrt{1-2x-2h}+\sqrt{1-2x}}=\frac{\sqrt{1-2x-2h}^2-\sqrt{1-2x}^2}{h(\sqrt{1-2x-2h}+\sqrt{1-2x})}=\frac{1-2x-2h-1+2x}{h(\sqrt{1-2x-2h}+\sqrt{1-2x})}=\frac{-2h}{h(\sqrt{1-2x-2h}+\sqrt{1-2x})}=\frac{-2}{\sqrt{1-2x-2h}+\sqrt{1-2x}}.$$
