$\begin{array}{l}a)\,\,\dfrac{1}{2\sqrt2 - 3\sqrt3}\\ =\dfrac{2\sqrt2 + 3\sqrt3}{(2\sqrt2 - 3\sqrt3)(2\sqrt2 + 3\sqrt3)}\\ = \dfrac{2\sqrt2 + 3\sqrt3}{8 - 27}\\ = - \dfrac{2\sqrt2 + 3\sqrt3}{19}\\ b)\,\,\sqrt{\dfrac{3-\sqrt5}{3 + \sqrt5}}\\ =\sqrt{\dfrac{(3-\sqrt5)^2}{(3 + \sqrt5)(3 - \sqrt5)}}\\ = \dfrac{3 - \sqrt5}{\sqrt{9 - 5}}\\ = \dfrac{3 - \sqrt5}{2}\\ c)\,\,\dfrac{\sqrt8}{\sqrt5 - \sqrt3}\\ = \dfrac{\sqrt8(\sqrt5 + \sqrt3)}{(\sqrt5 - \sqrt3)(\sqrt5 + \sqrt3)}\\ = \dfrac{2\sqrt2(\sqrt5 + \sqrt3)}{5 - 3}\\ = \sqrt2(\sqrt5 + \sqrt3)\\ d)\,\,\sqrt{\dfrac{2 - \sqrt3}{2 + \sqrt3}}\\ = \sqrt{\dfrac{(2 - \sqrt3)^2}{(2 + \sqrt3)(2 - \sqrt3)}}\\ = \dfrac{2 - \sqrt3}{\sqrt{4 - 3}}\\ = 2 - \sqrt3\end{array}$