Why is the limit of this function $0$? $$\lim_{x\to 0} \left(\sqrt{\dfrac{1}{x}+2} - \sqrt{\dfrac{1}{x}}\right)$$
I keep working this limit out as infinity as each term separately works out at infinity or non-existent but online calculators and the book solution tell me the limit is $0$.
Can anyone help me understand the steps to generate the right hand limit?

Multiply by $$\frac{\sqrt{\frac{1}{x}+2}+\sqrt{\frac{1}{x}}}{\sqrt{\frac{1}{x}+2}+\sqrt{\frac{1}{x}}}.$$ You get $$\frac{2}{\sqrt{\frac{1}{x}+2}+\sqrt{\frac{1}{x}}}$$ which tends to 0. (expanding in sight of binomial theorem is a pretty common trick)
