\[\boxed{\text{510\ (510).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]
\[\textbf{а)}\ \left( \frac{1^{\backslash x - x\sqrt{y}}}{x + x\sqrt{y}} + \frac{1^{\backslash x + x\sqrt{y}}}{x - x\sqrt{y}} \right) \cdot \frac{y - 1}{2} =\]
\[= \frac{2x}{x^{2} - x^{2}y} \cdot \frac{y - 1}{2} =\]
\[= \frac{x \cdot (y - 1)}{x^{2} \cdot (1 - y)} = - \frac{y - 1}{x \cdot (y - 1)} =\]
\[= - \frac{1}{x}\]
\[= \frac{2\sqrt{b}\sqrt{a} \cdot (a - b)}{2} =\]
\[= \sqrt{\text{ab}} \cdot (a - b) = a\sqrt{\text{ab}} - b\sqrt{\text{ab}}\text{.\ }\]