Take the numerator of the fraction and factor it out.
[tex]x^{2} + 3x - 4 = (x+4)(x-1)[/tex]
Your fraction should now look like this:
[tex] \frac{(x+4)(x-1)}{(x+4)} [/tex]
Because (x+4) is present in both the numerator and denominator, you can cross it out. You should be left with only (x-1) in the numerator.
x cannot equal -4, as if it is inputted in the denominator, -4 + 4 would equal 0. Dividing by 0 is impossible.