Rationalise the denominator and simplify :

$\dfrac{2}{\sqrt5 + \sqrt3}$

Since, the denominator = $\sqrt5 + \sqrt3$, its rationalizing factor = $\sqrt5 - \sqrt3$.

$\dfrac{2}{\sqrt5 + \sqrt3} = \dfrac{2}{\sqrt5 + \sqrt3} \times \dfrac{\sqrt5 - \sqrt3}{\sqrt5 - \sqrt3}\\[1em] = \dfrac{2(\sqrt5 - \sqrt3)}{(\sqrt5)^2 - (\sqrt3)^2} \\[1em] = \dfrac{2(\sqrt5 - \sqrt3)}{5 - 3} \\[1em] = \dfrac{2(\sqrt5 - \sqrt3)}{2}\\[1em] = (\sqrt5 - \sqrt3)$

Hence, $\dfrac{2}{\sqrt5 + \sqrt3} = (\sqrt5 - \sqrt3)$.