\[\frac{a}{3a + 3b}\ :\frac{a^{2}}{a^{2} - b^{2}} = \frac{a \cdot \left( a^{2} - b^{2} \right)}{3 \cdot (a + b) \cdot a^{2}} =\]
\[= \frac{(a - b)(a + b)}{3a(a + b)} = \frac{a - b}{3a}\]