# What are the asymptote(s) and hole(s), if any, of # f(x) =x/(x^4-x^2)#?

##### 1 Answer

It has horizontal asymptote

It has no slant asymptotes or holes.

#### Explanation:

Given:

#f(x) = x/(x^4-x^2)#

I like this question, since it provides an example of a rational function which takes a

#x/(x^4-x^2) = color(red)(cancel(color(black)(x)))/(color(red)(cancel(color(black)(x))) * x * (x^2-1)) = 1/(x(x-1)(x+1))#

Notice that in the simplified form, the denominator is

So

As

graph{x/(x^4-x^2) [-10, 10, -5, 5]}