Question

At which values does f(x)=2/3x(x-1)(x+5) have a vertical asymptote

Answer 1

The function $f(x)= \frac{2}{x(x-1)(x+5)}$ is undefined when the denominator is equal to 0:
$x(x-1)(x+5)=0 \\ x=0 \text{ or } x=1 \text{ or } x=-5$.
The domain of function f(x) is:
 $x\in (-\infty, -5)\cup (-5,0)\cup (0,1)\cup (1,\infty)$
and function f(x) has three vertical asymptotes
$x=-5, \\ x=0, \\ x=1$

Answer 2

$f(x) = \frac{2}{3x(x-1)(x+5)} \\ \\ Denominator x \neq 0, \\ \\x-1 \neq 0, x \neq 1, \\ \\x+5 \neq 5, x \neq -5. It should be 3 vertical asymptote x=0, x=1,x=-5$