What are the excluded values of x for x+4/-3x^2+12x+36

I will assume that you meant:

(x+4)/(-3x^2+12x+36)  factor the denominator...

(x+4)/(-3(x^2-4x-12))

To factor a quadratic of the form ax^2+bx+c you need to find two values, j and k, which satisfy two conditions...

jk=ac=-12 and j+k=b=-4 so j and k must be 2 and -6 and the factors are then:

(x+2)(x-6) so we are now left with:

(x+4)/(-3(x+2)(x-6))

The only restriction on this function is that division by zero is undefined, so x cannot equal -2 or 6

Ibelieve the answer would be 7, 13, 23