Question

What are the vertical asymptotes of the graph `y=(2x-6)/(x^3-x)`?

Answer 1

`x=0,x=1` and `x=-1`

The vertical asymptotes are where the denominator is equal to zero, because you can't divide by that.
So `x^3-x=0` is equivalent with `x(x^2-1)=0`, so `x=0` or `x^2=1`. By taking the square root of the second one, we find `x=1` and `x=-1`. So all the answers are `x=0,x=1` and `x=-1`.