What are the vertical asymptotes of the graph y=(2x-6)/(x^3-x)y=2x6x3x?

1 Answer
Dec 18, 2014

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

The vertical asymptotes are where the denominator is equal to zero, because you can't divide by that.
So x^3-x=0x3x=0 is equivalent with x(x^2-1)=0x(x21)=0, so x=0x=0 or x^2=1x2=1. By taking the square root of the second one, we find x=1x=1 and x=-1x=1. So all the answers are x=0,x=1x=0,x=1 and x=-1x=1.