# How do you find the asymptotes for #g(x) = (x^4 -81) /(x^3+3x^2 - x - 3)#?

##### 1 Answer

Vertical asymptotes at

#### Explanation:

Let us first factorize the numerator

and

=

Hence

Observe that when we have

Hence, we have a hole at

Further, when

Hence, we have vertical asymptotes at

Further as degree of numerator is just one more that of denominator, we should have an oblique or slanting asymptote.

As

and as

Hence, we have an oblique or slanting asymptote at

graph{(x^4-81)/(x^3+3x^2-x-3) [-84, 76, -33, 47]}