We have a horizontal asymptote at y = -1
This means that the ratio of the coefficients on the x variables are
1 / B = - 1 → B = -1
Since we have an x intercept at 4....this implies that 4 + A = 0 → A = -4
And finally, since we have a vertical asymptote at x = 3, this means that
-1(3) + C = 0
C = 3
So...our function is
x - 4
_____
-x + 3
A + B + C = -4 -1 + 3 = -2