Question

determine the vertical asymptote(s) of the following function. enter each asymptote as a separate equation, separating multiple asymptotes with a comma. if there are no vertical asymptotes, enter none.

$f(x)=\frac{5x - 6}{x^{3}-36x}$

Explanation:

Step1: Factor denominator

$x^3 - 36x = x(x^2 - 36) = x(x-6)(x+6)$

Step2: Find undefined points

Set denominator = 0: $x(x-6)(x+6)=0$ → $x=0,6,-6$

Step3: Check numerator at these x

Numerator $5x-6$: at $x=0$: $-6≠0$; $x=6$: $24≠0$; $x=-6$: $-36≠0$

Answer:

$x=-6, x=0, x=6$