finding the general term for $\displaystyle \frac{1}{\sqrt{2}+2}+\frac{1}{2\sqrt{3}+3\sqrt{2}} +...+\frac{1}{n\sqrt{n+1}+(n+1)\sqrt{n}}+...$

answer is:

$\displaystyle a_n=\frac{1}{n\sqrt{n+1}+(n+1)\sqrt{n}}=\frac{(n+1 )\sqrt{n}-n\sqrt{n+1}}{n(n+1)}=\frac{1}{\sqrt{n}}-\frac{1}{\sqrt{n+1}} $

how to derive $\displaystyle \frac{1}{\sqrt{n}}-\frac{1}{\sqrt{n+1}}$ from$\displaystyle \frac{(n+1)\sqrt{n}-n\sqrt{n+1}}{n(n+1)}$?