\[\boxed{\text{501\ (501).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]
\[при\ x = 3 + \sqrt{5};\ \ y = 3 - \sqrt{5}:\]
\[\frac{x^{2} - 3xy + y^{2}}{x + y + 2} =\]
\[= \frac{9 + 5 - 27 + 15 + 9 + 5}{8} =\]
\[= \frac{16}{8} = 2.\ \]