ANSWER
a=1 and b=-12
EXPLANATION
The hyperbola has a hole at:
x=3
and a vertical asymptote at x=-4.
This implies that the denominator of the rational function is
(x-3)(x+4)
We expand to get;
[tex] {x}^{2} + 4x - 3x - 12[/tex]
This simplifies to:
[tex]{x}^{2} + x - 12[/tex]
comparing to
[tex] {x}^{2} + ax + b[/tex]
We have a=1 and b=-12
