3. Given
$$
\begin{array}{l}
\left(\sqrt{x^{2}+201 \cdot 1}-x\right)\left(\sqrt{y^{2}+2011}-y\right) \\
=2011 . \\
\text { Then } \frac{x+2012 y}{2012 x+y}=(\quad) .
\end{array}
$$
(A) 2012
(B) 2011
(C) 1
(D) -1
3. D.

From the given, we have
$$
\sqrt{x^{2}+2011}-x=\sqrt{y^{2}+2011}+y \text {. }
$$

Similarly, $\sqrt{y^{2}+2011}-y=\sqrt{x^{2}+2011}+x$.
Adding the two equations yields $x+y=0$.
$$
\text { Then } \frac{x+2012 y}{2012 x+y}=\frac{2011 y}{2011 x}=\frac{y}{x}=-1 \text {. }
$$