Rationalise the denominator and simplify :

$\dfrac{1}{2\sqrt5 - \sqrt3}$

Since, the denominator = $2\sqrt5 - \sqrt3$, its rationalizing factor = $2\sqrt5 + \sqrt3$.

$\dfrac{1}{2\sqrt5 - \sqrt3} = \dfrac{1}{2\sqrt5 - \sqrt3} \times \dfrac{2\sqrt5 + \sqrt3}{2\sqrt5 + \sqrt3}\\[1em] = \dfrac{1(2\sqrt5 + \sqrt3)}{(2\sqrt5)^2 - (\sqrt3)^2} \\[1em] = \dfrac{2\sqrt5 + \sqrt3}{20 - 3} \\[1em] = \dfrac{2\sqrt5 + \sqrt3}{17}$

Hence, $\dfrac{1}{2\sqrt5 - \sqrt3} = \dfrac{2\sqrt5 + \sqrt3}{17}$.