Difference between revisions of "2013 AMC 10A Problems/Problem 8"
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What is the value of <math>\frac{2^{2014}+2^{2012}}{2^{2014}-2^{2012}} ?</math> | 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> | <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== | ==Solution== | ||
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Factoring out, we get: <math>\frac{2^{2012}(2^2 + 1)}{2^{2012}(2^2-1)}</math>. | Factoring out, we get: <math>\frac{2^{2012}(2^2 + 1)}{2^{2012}(2^2-1)}</math>. | ||
Revision as of 19:16, 1 February 2020
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 
.
See Also
| 2013 AMC 10A (Problems • Answer Key • Resources) | ||
| Preceded by Problem 7 |
Followed by Problem 9 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
| All AMC 10 Problems and Solutions | ||
| 2013 AMC 12A (Problems • Answer Key • Resources) | |
| Preceded by Problem 3 |
Followed by Problem 5 |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | |
| All AMC 12 Problems and Solutions | |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
