# What are the asymptote(s) and hole(s), if any, of # f(x) =x/(x^3-x)#?

##### 1 Answer

Holes 0

Vertical Asymptotes

Horizontal Asymptotes 0

#### Explanation:

An vertical asymptote or a hole is created by a point in which the domain is equal to zero i.e.

So either

An horizontal asymptote is created where the top and the bottom of the fraction don't cancel out. Whilst a hole is when you can cancel out.

So

So as the

For horizontal asymptotes one is trying to find what happens as x approaches infinity or negative infinity and whether it tends to a particular y value.

To do this divide both the numerator and denominator of the fraction by the highest power of

To do this we have to know two rules

and

For limits to negative infinty we have to make all the

So the horizontal asymptote as x approaches