Решите систему неравенств: x+5>=11/(x-5); x-1<=42/x.

\[\left\{ \begin{matrix} x + 5^{\backslash x - 5} \geq \frac{11}{x - 5} \\ x - 1^{\backslash x} \leq \frac{42}{x}\text{\ \ \ \ \ \ \ \ \ \ } \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ \ \ }\]

\[\left\{ \begin{matrix} \frac{(x + 5)(x - 5) - 11}{x - 5} \geq 0 \\ \frac{(x - 1)x - 42}{x} \leq 0\ \ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ }\]

\[\left\{ \begin{matrix} \frac{x^{2} - 25 - 11}{x - 5} \geq 0 \\ \frac{x^{2} - x - 42}{x} \leq 0\ \ \ \\ \end{matrix} \right.\ \]

\[\left\{ \begin{matrix} \frac{x^{2} - 36}{x - 5} \geq 0\ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ \frac{(x - 7)(x + 6)}{x} \leq 0 \\ \end{matrix} \right.\ \text{\ \ \ \ \ \ \ \ \ }\]

\[\left\{ \begin{matrix} \frac{(x - 6)(x + 6)}{x - 5} \geq 0 \\ \frac{(x - 7)(x + 6)}{x} \leq 0 \\ \end{matrix} \right.\ \]

\[Ответ:\left\{ - 6 \right\} \cup (0;5) \cup \lbrack 6;7\rbrack.\]