\[\left( \frac{a^{\backslash a}}{b} + \frac{b^{\backslash b}}{a} - 2^{\backslash ab} \right) \cdot \frac{1}{a - b} =\]
\[= \frac{a^{2} + b^{2} - 2ab}{\text{ab}} \cdot \frac{1}{a - b} =\]
\[= \frac{(a - b)^{2}}{\text{ab}(a - b)} = \frac{a - b}{\text{ab}}\]