\[f(x) = \frac{\sqrt{x - 1}}{\sqrt{x + 4}} - \frac{3x - 1}{x² - 6 - x},\ \ \]
\[\left\{ \begin{matrix} x - 1 \geq 0\ \ \ \ \ \ \ \ \ \\ x + 4 > 0\ \ \ \ \ \ \ \ \ \\ x^{2} - 6 - x \neq 0 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ }\]
\[\left\{ \begin{matrix} x \geq 1\ \ \ \\ x > - 4 \\ x \neq 3\ \ \ \\ x \neq - 2 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ }\]
\[\left\{ \begin{matrix} x \geq 1\ \ \ \\ x \neq 3\ \ \\ x \neq - 2 \\ \end{matrix} \right.\ \]
\[x^{2} - 6 - x = 0\]
\[x_{1} + x_{2} = 1,\ \ x_{1} = 3\]
\[x_{1} \cdot x_{2} = - 6,\ \ x_{2} = - 2\]
\[\Longrightarrow D(f) = \lbrack 1;3) \cup (3; + \infty).\]