\[\left( \frac{1^{\backslash y}}{x} - \frac{1^{\backslash x}}{y} \right)\ :\frac{y^{2} - x^{2}}{3xy} = \frac{y - x}{\text{xy}} \cdot \frac{3xy}{y^{2} - x²} =\]
\[= \frac{(y - x) \cdot 3}{(y - x)(y + x)} = \frac{3}{y + x}\]
\[x = \sqrt{2} - 8;\ \ y = \sqrt{\left( \sqrt{2} - 2 \right)^{2}}:\]
\[\frac{3}{\left| \sqrt{2} - 2 \right| + \sqrt{2} - 8} =\]
\[= \frac{3}{2 - \sqrt{2} + \sqrt{2} - 8} = - \frac{3}{6} = - 0,5.\]
\[Ответ:\ - 0,5.\]