Verified answer

[tex]\displaystyle\bf\\11)\\\\\frac{1}{x-2} \geq \frac{5}{x} \\\\\\\frac{1}{x-2} -\frac{5}{x} \geq 0\\\\\\\frac{x-5\cdot(x-2)}{x\cdot(x-2)} \geq 0\\\\\\\frac{x-5x+10}{x(x-2)} \geq0\\\\\\\frac{-4x+10}{x(x-2)} \geq 0\\\\\\\frac{x-2,5}{x(x-2)} \leq 0\\\\\\\left[\begin{array}{ccc}x-2,5=0\\x\neq 0\\x-2\neq 0\end{array}\right\\\\\\\left[\begin{array}{ccc}x=2,5\\x\neq 0\\x\neq 2\end{array}\right[/tex]

- - - - - (0) + + + + + (2) - - - - - [2,5] + + + + +

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Ответ : x ∈ ( - ∞ : 0) ∪ (2 ; 2,5]

[tex]\displaystyle\bf\\12)\\\\\frac{4}{x-3} \geq \frac{6}{x} \\\\\\\frac{4}{x-3} -\frac{6}{x} \geq 0\\\\\\\frac{4x-6\cdot(x-3)}{x\cdot(x-3)} \geq 0\\\\\\\frac{4x-6x+18}{x(x-3)}\geq 0\\\\\\\frac{-2x+18}{x(x-3)} \geq 0\\\\\\\frac{x-9}{x(x-3)} \leq0\\\\\\\left[\begin{array}{ccc}x-9=0\\x\neq 0\\x-3\neq 0\end{array}\right\\\\\\\left[\begin{array}{ccc}x=9\\x\neq 0\\x\neq 3\end{array}\right[/tex]

- - - - - (0) + + + + + (3) - - - - - [9]+ + + + +

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Ответ : x ∈ (- ∞ ; 0) ∪ (3 ; 9]