\[\ \frac{4a^{2} - 1}{a^{2} - 9}\ :\frac{6a + 3}{a + 3} =\]
\[= \frac{(2a + 1)(2a - 1) \cdot (a + 3)}{(a - 3)(a + 3) \cdot 3 \cdot (2a + 1)} =\]
\[= \frac{2a - 1}{3 \cdot (a - 3)}\]