Difference between revisions of "2013 AMC 10A Problems/Problem 8"
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+ | ==Problem== | ||
+ | What is the value of <math>\frac{2^{2014}+2^{2012}}{2^{2014}-2^{2012}} ?</math> | ||
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+ | <math> \textbf{(A)}\ -1 \qquad\textbf{(B)}\ 1 \qquad\textbf{(C)}\ \frac{5}{3} \qquad\textbf{(D)}\ 2013 \qquad\textbf{(E)}\ 2^{4024} </math> | ||
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+ | ==Solution== | ||
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+ | Factoring out, we get: <math>\frac{2^{2012}(2^2 + 1)}{2^{2012}(2^2-1)} ?</math> | ||
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+ | Cancelling out the <math>2^{2012}</math> from the numerator and denominator, we see that it simplifies to <math>\frac{5}{3}</math>, <math>\textbf{(C)}</math>. |
Revision as of 19:57, 7 February 2013
Problem
What is the value of
Solution
Factoring out, we get:
Cancelling out the from the numerator and denominator, we see that it simplifies to
,
.