Question: Rationalize the denominators and simplify: $\dfrac{3}{\sqrt{5} - \sqrt{2}}$

Solution:
Given,

$= \dfrac{3}{\sqrt{5} - \sqrt{2}}$

$= \dfrac{3}{\sqrt{5} - \sqrt{2}} × \dfrac{\sqrt{5} + \sqrt{2}}{\sqrt{5} + \sqrt{2}}$

$= \dfrac{3(\sqrt{5} + \sqrt{2}}{(\sqrt{5})^2 - (\sqrt{2})^2}$

$= \dfrac{3(\sqrt{5} + \sqrt{2})}{(5-2)}$

$= \dfrac{3(\sqrt{5} + \sqrt{2})}{3}$

$= \sqrt{5} + \sqrt{2}$
= Answer