\[\left( \frac{\sqrt{5}}{x} + \frac{\sqrt{5}}{y} \right):\frac{\sqrt{3}}{x - y} =\]
\[= \frac{\sqrt{5}(x + y)(x - y)}{xy \cdot \sqrt{3}} =\]
\[= \frac{\sqrt{5}\left( x^{2} - y^{2} \right)}{\sqrt{3}\text{xy}}\]
\[x = \sqrt[4]{9 - 2\sqrt{14}};\ \ \ \]
\[y = \sqrt[4]{9 + 2\sqrt{14}}:\]
\[= \sqrt{9 - 2\sqrt{14}} + \sqrt{9 + 2\sqrt{14}} =\]
\[xy = \sqrt[4]{9 - 2\sqrt{14}} \cdot \sqrt[4]{9 - 2\sqrt{14}} =\]
\[= \sqrt[4]{\left( 9 - 2\sqrt{14} \right)\left( 9 + 2\sqrt{14} \right)} =\]
\[= \sqrt[4]{\left( \sqrt{2} - \sqrt{7} \right)^{2}\left( \sqrt{2} + \sqrt{7} \right)^{2}} =\]
\[= \sqrt[4]{\left( \left( \sqrt{2} - \sqrt{7} \right)\left( \sqrt{2} + \sqrt{7} \right) \right)^{2}}\]
\[= \sqrt[4]{\left( \left( \sqrt{2} \right)^{2} - \left( \sqrt{7} \right)^{2} \right)^{2}} =\]
\[= \sqrt[4]{(2 - 7)^{2}} = \sqrt[4]{( - 5)^{2}} = \sqrt{5}\]
\[\frac{\sqrt{5}\left( x^{2} - y^{2} \right)}{\sqrt{3}\text{xy}} = \frac{\sqrt{5} \cdot \left( - 2\sqrt{2} \right)}{\sqrt{3} \cdot \sqrt{5}} =\]
\[= - \frac{2\sqrt{2}}{\sqrt{3}} = - \frac{2\sqrt{6}}{3}.\]