User:Nessuno97/sandbox

$$\begin{align}(\sqrt{a}+\sqrt{b})(\sqrt{a}- \sqrt{b}) &= \sqrt{a}\sqrt{a} - \sqrt{a}\sqrt{b} + \sqrt{b}\sqrt{a} - \sqrt{b}\sqrt{b}\\ & = a - b \end{align} (\sqrt{a}+\sqrt{b})^{-1} = \frac{1}{(\sqrt{a}+\sqrt{b})} = \frac{1}{\sqrt{a}+\sqrt{b}}\cdot \frac{\sqrt{a}-\sqrt{b}}{\sqrt{a}-\sqrt{b}} = \frac{\sqrt{a}- \sqrt{b}} {a - b}$$