radicals - Finding limit (or rather simplifying) a specific function

The question is asking to find the limit of:

$$\lim_{x \to 0}\frac{\sqrt{1+x} - \sqrt{1-x}}{x}$$ If we plug x into the equation, both the denominator and numerator become 0 so I have to simplify the equation somehow. The answer according to the textbook is 1 although I have no clue as to how I would get that answer myself. Any hints are greatly appreciated!

Answer

Hint:

$$\frac{\sqrt{1+x}-\sqrt{1-x}}{x}=\frac{(\sqrt{1+x}-\sqrt{1-x})(\sqrt{1+x}+\sqrt{1-x})}{x(\sqrt{1+x}+\sqrt{1-x})}=\frac{1+x-(1-x)}{x(\sqrt{1+x}+\sqrt{1-x})}=\frac{2}{\sqrt{1+x}+\sqrt{1-x}}.$$