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