2013 AMC 10A Problems/Problem 8

Problem

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

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

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

Let $x=2^{2012}$

Then the given expression is equal to $\frac{4x+x}{4x-x}=\frac{5x}{3x}=\boxed{\textbf{(C) }\frac{5}{3}}$

~sugar_rush

2013 AMC 10A (Problems • Answer Key • Resources)
Preceded by Problem 7	Followed by Problem 9
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2013 AMC 12A (Problems • Answer Key • Resources)
Preceded by Problem 3	Followed by Problem 5
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All AMC 12 Problems and Solutions