$\begin{array}{l}S = \left(\dfrac{1}{2 - \sqrt5} + \dfrac{2}{\sqrt5 + \sqrt3}\right) : \dfrac{1}{\sqrt{21 - 12\sqrt3}}\\ = \left(\dfrac{2 + \sqrt5}{4 - 5} + \dfrac{2(\sqrt5 - \sqrt3)}{5 - 3}\right).\sqrt{12 - 2.3.2\sqrt3 + 9}\\ = (-2 - \sqrt5 + \sqrt5 - \sqrt3).\sqrt{(2\sqrt3 - 3)^2}\\ = (2 + \sqrt3)(3 - 2\sqrt3)\\ = \sqrt3(\sqrt3 + 2)(\sqrt3 - 2)\\ = \sqrt3(3 - 4)\\ = - \sqrt3\\ U = \dfrac{2}{\sqrt5 + 1}\cdot\sqrt{\dfrac{2}{3 - \sqrt5}}\\ = \dfrac{2(\sqrt5 - 1)}{5 - 1}\cdot\sqrt{\dfrac{4}{6 - 2\sqrt5}}\\ = \dfrac{\sqrt5 - 1}{2}\cdot\dfrac{2}{\sqrt{(\sqrt5 - 1)^2}}\\ = \dfrac{\sqrt5 - 1}{2}\cdot\dfrac{2}{\sqrt5 - 1} = 1\\ W = \dfrac{5\sqrt3}{\sqrt{3 - \sqrt5} - \sqrt3}- \dfrac{5\sqrt3}{\sqrt{3 - \sqrt5} + \sqrt3}\\ = \dfrac{5\sqrt6}{\sqrt{6 - 2\sqrt5} - \sqrt6}- \dfrac{5\sqrt6}{\sqrt{6 - 2\sqrt5} + \sqrt6}\\ = 5\sqrt6\left(\dfrac{1}{\sqrt{(\sqrt5 - 1)^2} - \sqrt6}- \dfrac{1}{\sqrt{(\sqrt5 - 1)^2} + \sqrt6}\right)\\ = 5\sqrt6\left(\dfrac{1}{\sqrt5 - 1 - \sqrt6}- \dfrac{1}{\sqrt5 - 1 + \sqrt6}\right)\\ = 5\sqrt6\left[\dfrac{\sqrt5 - 1 + \sqrt6 - (\sqrt5 - 1 - \sqrt6)}{(\sqrt5 - 1 - \sqrt6)(\sqrt5 - 1 + \sqrt6)}\right]\\ = 5\sqrt6.\dfrac{2\sqrt6}{(\sqrt5 - 1)^2 - 6}\\ = \dfrac{60}{2\sqrt5}\\ = 6\sqrt5\end{array}$
