Question

x+3/x^-x-12 + 2/x+3 = 1/x-4

Answer 1

Please add parentheses where needed for clarification.

I suspect your first term is actually
(x+3)/(x^2 -x -12) = (x+3)/[(x+3)(x-4)]
= 1/(x-4)

You need parentheses in other places as well.

Answer 2

This is how the problem looks:
(x+3)/(x^2-x-12) + (2/x + 3)= (1)/(x-4)