We have a "zero" at x = 4
This means that , in the numerator, 4 + A = 0
So A = -4
Also....we have a horizontal asymptote at y = -1
Looking at the coefficients on the x variables in the numerator and denominato, taking their ratio and setting it equal to this asymptote, we have that
1 / B = -1
So B = -1
And we have a vertical asymprore at x = 3
This means that, in the denominator, -1 (3) + C = 0 → C = 3
A + B + C =
-4 - 1 + 3 =
-2
See the graph here to confirm this : https://www.desmos.com/calculator/tx6zbax7ra