What is the value of 2^2014 + 2^20122^2014 - 2^2012?

2013 AMC 12A Problem 4

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What is the value of

\dfrac{2^{2014} + 2^{2012}}{2^{2014} - 2^{2012}}?

-1

1

\dfrac{5}{3}

2013

2^{4024}

Factor

2^{2012}

out of both the numerator and the denominator

The ratio reduces to

\dfrac{2^2 + 1}{2^2 - 1}

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.