AMC12 2013 A
AMC12 2013 A · Q4
AMC12 2013 A · Q4. It mainly tests Exponents & radicals.
What is the value of $\dfrac{2^{2014}+2^{2012}}{2^{2014}-2^{2012}}$?
$\dfrac{2^{2014}+2^{2012}}{2^{2014}-2^{2012}}$ 的值是多少？
(A)
-1
-1
(B)
1
1
(C)
\frac{5}{3}
\frac{5}{3}
(D)
2013
2013
(E)
$2^{4024}$
$2^{4024}$
Answer
Correct choice: (C)
正确答案：（C）
Solution
Answer (C): Factoring $2^{2012}$ from each of the terms and simplifying gives
\[
\frac{2^{2012}(2^2+1)}{2^{2012}(2^2-1)}=\frac{4+1}{4-1}=\frac{5}{3}.
\]
答案（C）：从每一项中提取公因式 $2^{2012}$ 并化简可得
\[
\frac{2^{2012}(2^2+1)}{2^{2012}(2^2-1)}=\frac{4+1}{4-1}=\frac{5}{3}.
\]
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