So I am trying to find the behaviour of this function around an asymptote at $x=0$.
$a>0$
$y=\frac{(x-a)(x^2+a)}{x^2}$
I know that as $x \to 0^+$, $y \to -\infty $ and $x \to 0^-$, $y \to -\infty $.
I've tried dividing the top and bottom of $y$ by $x^2$ and ended with:
$x-a+\frac{a}{x}-\frac{a^2}{x^2}$
Which does not help me as I end with $\infty -\infty$. Any help would be greatly appreciated.