# What are the oblique asymptote of P(x)= 4x^5/(x^3-1)?

Sep 9, 2015

The function has no oblique (linear) asymptotes.

#### Explanation:

When we do the division, we get:

$P \left(x\right) = \frac{4 {x}^{5}}{{x}^{3} - 1} = 4 {x}^{2} + \frac{4 {x}^{2}}{{x}^{3} - 1}$

Although $P \left(x\right)$ does get arbitrarily close to the parabola $y = 4 {x}^{2}$, a parabola is not an oblique asymptote.