AMC 10 2008a Problem 7

The fraction $$\frac{\left(3^{2008}\right)^2-\left(3^{2006}\right)^2}{\left(3^{2007}\right)^2-\left(3^{2005}\right)^2}$$ simplifies to which of the following? $\mathrm{(A)}\ 1 \mathrm{(B)}\ \frac{9}{4} \mathrm{(C)}\ 3 \mathrm{(D)}\ \frac{9}{2} \mathrm{(E)}\ 9$