\[\frac{b - 1}{a^{2}} \cdot \left( \frac{a^{\backslash b}}{b - 1} - \frac{a^{\backslash b - 1}}{b} \right) =\]
\[= \frac{b - 1}{a²} \cdot \frac{ab - ab + a}{b(b - 1)} = \frac{(b - 1)a}{a²b(b - 1)} = \frac{1}{\text{ab}}\]