\[\left( a^{- 2} - b^{- 2} \right)(a - b)^{- 1} =\]
\[= \left( \frac{1}{a^{2}} - \frac{1}{b^{2}} \right)\left( \frac{1}{a - b} \right) =\]
\[= \frac{b^{2} - a^{2}}{a^{2}b^{2}} \cdot \frac{1}{a - b} =\]
\[= \frac{- (a - b)(b + a)}{a²b²(a - b)} = - \frac{a + b}{a²b²}\]