Difference between revisions of "2013 AMC 10A Problems/Problem 8"

Revision as of 18:57, 7 February 2013

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

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

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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+==Problem==
+What is the value of <math>\frac{2^{2014}+2^{2012}}{2^{2014}-2^{2012}} ?</math>
+<math> \textbf{(A)}\ -1 \qquad\textbf{(B)}\ 1  \qquad\textbf{(C)}\ \frac{5}{3} \qquad\textbf{(D)}\ 2013 \qquad\textbf{(E)}\ 2^{4024} </math>
+==Solution==
+Factoring out, we get: <math>\frac{2^{2012}(2^2 + 1)}{2^{2012}(2^2-1)} ?</math>
+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>.