[latex] \left \{ {{ \frac{x-1}{x-6 } \geq 0 } \atop {x+1 \geq 0}} \right. [/latex] Пожалуйста

[latex] \left \{ {{\frac{x-1}{x-6}\ge0} \atop {x+1\ge0}} \right. ,\\x-6\ne0,\\x\ne6;\\\\ \left \{ {{x-1\ge0} \atop {x+1\ge0}} \right.,\\\\ \left \{ {{x\ge1} \atop {x\ge-1}} \right.\ \Longrightarrow\ x\ge1,\\\\ \left \{ {{x\ge1} \atop {x\ne6}} \right.\ \Longrightarrow\ 1\le x\ \textless \ 6,\ x\ \textgreater \ 6.\\\\OTBET:\ [1;\ 6),\ (6;\ \infty).[/latex]