AMC10 2013 A

AMC10 2013 A · Q8

AMC10 2013 A · Q8. It mainly tests Exponents & radicals, Manipulating equations.

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

$\frac{2^{2014}+2^{2012}}{2^{2014}-2^{2012}}$ 的值是多少？

(A) $-1$ $-1$

(B) 1 1

(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）：从每一项中提取出 $2^{2012}$ 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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