2013 AMC 12A Problem 4

Factoring $2^{2012}$ from each term gives $$\dfrac{2^{2012}(2^2 + 1)}{2^{2012}(2^2 - 1)} = \dfrac{4 + 1}{4 - 1} = \dfrac{5}{3}.$$ Thus, the correct answer is C.