For what values of x, if any, does f(x) = 1/((5x+8)(x+4)  have vertical asymptotes?

Mar 22, 2018

$x$ = $- 4$ and $- \frac{8}{5}$

Explanation:

So, a vertical asymptote is a line that extends vertically to infinity. If we notice, it implies that the y co-ordinate of the curve much reach Infinity.

We know that infinity = $\frac{1}{0}$

So, when compared with $f \left(x\right)$, it implies that the denominator of $f \left(x\right)$ should be zero. Hence,

$\left(5 x + 8\right) \left(x + 4\right)$ = $0$

This is a quadratic equation whose roots are $- 4$ and $- \frac{8}{5}$.

Hence, at $x$ = $- 4$, $- \frac{8}{5}$ we have vertical asymptotes