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 $a+b+c$.

Guest Aug 29, 2017

#1**+1 **

\( $f(x)=\frac{2x}{x^2-5x-14}$\)

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

CPhill Aug 29, 2017