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2013 AMC 10A Problems/Problem 8

Revision as of 18:57, 7 February 2013 by Countingkg (talk | contribs)

Problem

What is the value of $\frac{2^{2014}+2^{2012}}{2^{2014}-2^{2012}} ?$


$\textbf{(A)}\ -1 \qquad\textbf{(B)}\ 1 \qquad\textbf{(C)}\ \frac{5}{3} \qquad\textbf{(D)}\ 2013 \qquad\textbf{(E)}\ 2^{4024}$


Solution

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 $\frac{5}{3}$, $\textbf{(C)}$.

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