A2. Let $x=2^{2013}$. What is the value of the expression

$$
x-\sqrt{x^{2}+1}+\frac{1}{\sqrt{x^{2}+1}+x} ?
$$

equal to
(A) -1
(B) 0
(C) 1
(D) $2^{2013}$
(E) 2
A2. If we bring the expression to a common denominator and rearrange, we get

$$
\frac{\left(x+\sqrt{x^{2}+1}\right)\left(x-\sqrt{x^{2}+1}\right)+1}{\sqrt{x^{2}+1}+x}=\frac{\left(x^{2}-\left(x^{2}+1\right)\right)+1}{\sqrt{x^{2}+1}+x}=0 .
$$

The correct answer is $B$.