Factoring out, we get: $\frac{2^{2012}(2^2 + 1)}{2^{2012}(2^2-1)}$.
Cancelling out the $2^{2012}$ from the numerator and denominator, we see that it simplifies to $\boxed{\textbf{(C) }\frac{5}{3}}$.

$\frac{2^{2014}+2^{2012}}{2^{2014}-2^{2012}}$
We can factor a ${2^{2012}}$ out of the numerator and denominator to obtain
$\frac{2^{2012}*(2^2+1)}{2^{2012}*(2^2-1)}$
The ${2^{2012}}$ cancels, so we get
$\frac{(2^2+1)}{(2^2-1)}=\frac{5}{3}$, which is $C$