# How do you find the asymptotes for #(x^3-x)/(x^3-4x)#?

##### 1 Answer

Horizontal asymptote:

Vertical asymptote:

Discontinuity at

#### Explanation:

Given

Let's start by factoring the function

If you notice, there is a same factor of

Discontinuity aka hole on the graph at

**Discontinuity** at #(0, 1/4)

**Horizontal asymptote** :

Since degree and coefficient of the numerator and denominator are the same, hence the horizontal asymptote is

**Vertical asymptote**

Set the denominator of the reduce function equal to zero

graph{(x^3-x)/(x^3-4x) [-7.024, 7.024, -3.51, 3.51]}