# upper and lower bounds of a set with two variables

of two sets - $A={\frac{n-k^{2}}{n^{2}+k^{3}}$ , $n,k \in \mathbb{N}}$ and $B={\frac{m^{2}-n}{m^{2}+n^{2}}$, $n,m \in \mathbb{N}, m>n}$.
definition. I assume that for the supremum of B $\epsilon>0$ and
$\frac{m^{2}-n}{m^{2}+n^{2}} >\epsilon$ and I want to show that for all $n>n_\epsilon$. How can I do it?