To simplify the expression, we can start by factoring out the common factor of 4 from the numerator:

4x - 12 = 4(x - 3)

Now, let's simplify the denominator by using the difference of squares formula:

(√a + 3)(√a - 3) = (√a)^2 - (3)^2 = a - 9

Putting it all together, the simplified expression is:

4(x - 3) / (a - 9)