\[f(x) = \sqrt{x + 2\ } + \frac{x - 7}{x^{2} - 4}\ \]
\[\left\{ \begin{matrix} x + 2 \geq 0 \\ x^{2} \neq 4\ \ \ \ \ \ \\ \end{matrix}\text{\ \ \ \ \ \ \ \ } \right.\ \]
\[\left\{ \begin{matrix} x \geq - 2 \\ x \neq \pm 2 \\ \end{matrix} \right.\ \]
\[\Longrightarrow ( - 2;\ \ 2) \cup (2;\ + \infty).\]