Hey I have the problem

Determine whether the sequence converges or diverges. If it converges, find the limit.

$\displaystyle \lim_{n \to \infty}a_n = \frac{7+4n^2}{n+n^2}$

To me it looks like a $\displaystyle \frac{\infty}{\infty}$ situation and doesn't converge but do i have to do some algebraic manipulation to be able to take the limit and find what it converges to? Thanks.