I assume you mean (x-7) / (x^2 - 4x - 12), right?

If so the first step is to factor the quadratic expression in the denominator. It factors into (x-6)(x+2).

Since there are no (binomial) factors in common between the numerator and the denominator, this expression can not be further simplified.

The domain for a polynomial expression, like the this one, is the set of all real numbers except for those values that would make the denominator equal to zero. In this specific case, if x = 6 or x = -2, the denominator would equal zero.

So, the domain of this function is (- infinity, -2) U (-2, 6) U (6, positive infinity).