The graph of $f(x)=\frac{2x}{x^2-5x-14}$ has vertical asymptotes $x=a$ and $x=b$, and horizontal asymptote $y=c$. Find $a+b+c$.
\( $f(x)=\frac{2x}{x^2-5x-14}$\)
Factoring the denominator, we have
2x / [ (x - 7) ( x + 2) ]
Note that x = 7 or x = -2 make the denominator undefined.....so these are the vertical asymptotes
And since the degree of the poynominal in the numerator is one less than that of the denominator, we will have a horizontal asymptote at y = 0
So.....the sum of the asymptotes is = 7 - 2 + 0 = 5