$(\frac{1}{(a - 3)^2} - \frac{6}{9 - a^2} + \frac{9}{(a + 3)^2}) : \frac{4(2a - 3)^2}{(a^2 - 9)(a^2 - 27)} - \frac{2a^2}{9 - a^2} = (\frac{1}{(a - 3)^2} + \frac{6}{a^2 - 9} + \frac{9}{(a + 3)^2}) * \frac{(a^2 - 9)(a^2 - 27)}{4(2a - 3)^2} - \frac{2a^2}{9 - a^2} = (\frac{1}{(a - 3)^2} + \frac{6}{(a - 3)(a + 3)} + \frac{9}{(a + 3)^2}) * \frac{(a^2 - 9)(a^2 - 27)}{4(2a - 3)^2} - \frac{2a^2}{9 - a^2} = \frac{(a + 3)^2 + 6(a^2 - 9) + 9(a - 3)^2}{(a - 3)^2(a + 3)^2} * \frac{(a - 3)(a + 3)(a^2 - 27)}{4(2a - 3)^2} - \frac{2a^2}{9 - a^2} = \frac{a^2 + 6a + 9 + 6a^2 - 54 + 9(a^2 - 6a + 9)}{(a - 3)(a + 3)} * \frac{a^2 - 27}{4(2a - 3)^2} - \frac{2a^2}{9 - a^2} = \frac{7a^2 + 6a - 45 + 9a^2 - 54a + 81}{(a - 3)(a + 3)} * \frac{a^2 - 27}{4(2a - 3)^2} - \frac{2a^2}{9 - a^2} = \frac{16a^2 - 48a + 36}{(a - 3)(a + 3)} * \frac{a^2 - 27}{4(2a - 3)^2} - \frac{2a^2}{9 - a^2} = \frac{(4a - 6)^2}{(a - 3)(a + 3)} * \frac{a^2 - 27}{4(2a - 3)^2} + \frac{2a^2}{a^2 - 9} = \frac{(2(2a - 3))^2}{(a - 3)(a + 3)} * \frac{a^2 - 27}{4(2a - 3)^2} + \frac{2a^2}{a^2 - 9} = \frac{4(2a - 3)^2}{(a - 3)(a + 3)} * \frac{a^2 - 27}{4(2a - 3)^2} + \frac{2a^2}{a^2 - 9} = \frac{a^2 - 27}{a^2 - 9} + \frac{2a^2}{a^2 - 9} = \frac{a^2 - 27 + 2a^2}{a^2 - 9} = \frac{3a^2 - 27}{a^2 - 9} = \frac{3(a^2 - 9)}{a^2 - 9} = 3$