# How do you find the vertical, horizontal or slant asymptotes for #(4+x^4)/(x^2-x^4)#?

##### 1 Answer

Vertical asymptotes at

#### Explanation:

We have vertical asymptotes for

Here in denominator, we have

Hence, we have vertical asymptotes at

We have horizontal asymptote when

Here

=

=

Hence we have a horizontal asymptote

Slant asymptote is there when degree of numerator is just one more than that of denominator. Here we do not have a slant asymptote.

graph{(4+x^4)/(x^2-x^4) [-10, 10, -10, 25]}

As an example of slant asymptote consider

=

=

graph{(4+x^5)/(x^2-x^4) [-10, 10, -10, 25]}

**Graphs not drawn to scale.**