Question

Simplificar:

$\frac{3}{ \sqrt{2} - \sqrt{3} + {} \sqrt{5} }$

Answer 1

Asumiendo que quieres racionalizar
$\begin{matrix} \dfrac{3}{\sqrt{2}-\sqrt{3}+\sqrt{5}} \cdot \dfrac{\sqrt{2}+\sqrt{3}+\sqrt{5}}{\sqrt{2}+\sqrt{3}+\sqrt{5}} &=& \dfrac{3(\sqrt{2}+\sqrt{3}+\sqrt{5})}{(\sqrt{2}+\sqrt{5})^2-3}\\\\ &=& \dfrac{3(\sqrt{2}+\sqrt{3}+\sqrt{5})}{2\sqrt{10}-4}\cdot{}\dfrac{2\sqrt{10}+4}{2\sqrt{10}+4}\\\\ &=& \frac{1}{4}(\sqrt{2}+\sqrt{3}+\sqrt{5})}(\sqrt{10}+2) \end{matrix}$