3. The minimum value of the fraction $\frac{5 x^{2}+30 x y+51 y^{2}}{x^{2}+6 x y+11 y^{2}}$ is ( ).
(A) -5
(B) -3
(C) 5
(D) 3
3. D.
$$
\begin{array}{l}
\text { Original expression }=5-\frac{4 y^{2}}{x^{2}+6 x y+11 y^{2}} \\
=5-\frac{4 y^{2}}{(x+3 y)^{2}+2 y^{2}} \\
=5-\frac{4}{\left(\frac{x}{y}+3\right)^{2}+2} .
\end{array}
$$

When $\frac{x}{y}=-3$, the original expression takes the minimum value 3.