А^3-8а^2-3а-6/а^2-4

To simplify the expression (a^3 - 8a^2 - 3a - 6) / (a^2 - 4), we can first factor the numerator and denominator.

Numerator: a^3 - 8a^2 - 3a - 6 Denominator: a^2 - 4

Factor the numerator: (a^3 - 8a^2) - (3a + 6) a^2(a - 8) - 3(a + 2)

Now factor the denominator: (a^2 - 4) (a - 2)(a + 2)

Now substitute the factored numerator and denominator back into the original expression: [(a^2 - 8)(a - 2) - 3(a + 2)] / [(a - 2)(a + 2)]

Next, cancel out common factors between the numerator and denominator: [(a - 2)(a^2 - 8 - 3)] / [(a - 2)(a + 2)]

(a - 2) cancels out in the numerator and denominator, leaving us with: (a^2 - 11) / (a + 2)

Therefore, the simplified expression is (a^2 - 11) / (a + 2).