Полное решение!11!Решите неравенство: [latex] \frac{ x^{2} -7x+6}{x-2} [/latex][latex] \leq 0[/latex]

[latex]\frac{x^2-7x+6}{x-2} \leq 0\\\\ x^2-7x+6=(x-1)(x-6)\\\\\ \frac{(x-1)(x-6)}{x-2} \leq 0\\\\ x \neq 2\\\\ [/latex] [latex]1) \left \{ {{(x-1)(x-6) \geq 0} \atop {x-2<0}} \right. \\\\ 2) \left \{ {{(x-1)(x-6) \leq 0 } \atop {x-2>0}} \rigaht. \\\\ [/latex] Первое неравенство  [latex]1) \left \{ {{(x-1)(x-6) \geq 0} \atop {x-2<0}} \right. \\\\ 1) \left \{ {{x \leq 1 \ ; \ x \geq 6} \atop {x<2}} \right. \\\\ 1) \left \{ {{x \geq 1 ; x \leq 6} \atop {x<2}} \right. [/latex]  Получаем решение  [latex]x \in (\infty;1)[/latex] Второе неравенство   [latex] \left \{ {{(x-1)(x-6) \leq 0 } \atop {x>2}} \right. \\\\ \left \{ {{x \leq 1 ; \ \ x \geq 6} \atop {x>2}} \right. \\\\ \left \{ {{x \geq 1; x \leq 6} \atop {x<2}} \right. [/latex]   Получаем решение   [latex]x \in (2;6]\\[/latex] Объединяя    [latex] x \in (-\infty;1) \ \ \cup \ \ \ (2;6][/latex]