((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).
((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).