Respuesta :

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

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