Please help me with this problem.

\(\text{If $f(x)=\frac{x+4}{x^2+ax+b}$, and $f(x)$ has two vertical asymptotes at $x=1$ and $x=-2$, find the sum of $a$ and $b$. }\)

Thanks!

Since we have vertical asymptotes at x = 1 and x = - 2, the denominator has the form

(x - 1) (x + 2) since x = 1 and x = -2 will make the denominator 0

So....expanding....we have x^2 - 1x + 2x - 2 = x^2 + 1x - 2 = x^2 + ax + b

So

a =1 and b =-2

And a + b = 1 + (-2) = -1

Thanks a lot!!