\[\boxed{\text{186\ (186).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]
\[y = \frac{2x + 5}{x - 3} = \frac{2x - 6 + 11}{x - 3} =\]
\[= \frac{2x - 6}{x - 3} + \frac{11}{x - 3} =\]
\[= \frac{2 \cdot (x - 3)}{x - 3} + \frac{11}{x - 3} =\]
\[= 2 + \frac{11}{x - 3};\]
\[Дробь\ \ \ \frac{11}{x - 3}\text{\ \ }должна\ быть\ \]
\[натуральной \Longrightarrow\]
\[\Longrightarrow \left\{ \begin{matrix} 11 = x - 3 \\ 1 = x - 3\ \ \ \\ \end{matrix} \right.\ \Longrightarrow \left\{ \begin{matrix} x = 14 \\ x = 4\ \ \\ \end{matrix} \right.\ \]
\[x = 14:\]
\[y = 2 + \frac{11}{14 - 3} = 2 + 1 = 3.\]
\[x = 4:\]
\[y = 2 + \frac{11}{4 - 3} = 2 + 11 = 13.\]
\[Искомые\ точки:\ \ (14;3)\ и\ \]
\[\ (4;13).\]