((а^2 -9)/(а^2 -2а+4)) ÷ (а+3)/(9а^3 +72)

Simplify the expression by factoring and canceling out common terms:

((a^2 - 9)/((a - 2)^2)) ÷ (a + 3)/(9a^3 + 72)
((a + 3)(a - 3)/((a - 2)^2)) ÷ (a + 3)/(9(a^3 + 8))
((a + 3)(a - 3)/((a - 2)^2)) (9(a^3 + 8))/(a + 3)
Cancel out (a + 3):
(a - 3)/((a - 2)^2) 9(a^3 + 8)
(a - 3)* 9(a^3 + 8)/((a - 2)^2)
(9a^4 - 27 + 72a - 216)/((a - 2)^2)
9a^4 + 72a - 243/((a - 2)^2)

Therefore, the simplified expression is (9a^4 + 72a - 243)/((a - 2)^2).