Системи неравенства

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[ammornil]

[tex]\begin{aligned} \begin{array}{|l} \frac{\normalsize{x^{2}+7x+6}}{\normalsize{x^{2}}}\ge 6 \\ 2x^{2}+5x+2>0 \\ \frac{\normalsize{x^{2}-2x-1}}{\normalsize{x^{2}+2}}<0 \end{array} \\ & \text{ДМ: } \begin{array}{|l} x^{2}\ne 0 \\ x^{2}+2\ne 0 \end{array} \Rightarrow x \in (-\infty; 0) \cup (0;+\infty) \\ \begin{array}{|l} x^{2}+7x+6-6x^{2}\ge 0 \\ 2x^{2}+5x+2>0 \\ x^{2}-2x-1<0 \end{array} \Leftrightarrow \begin{array}{|l} 5x^{2}-7x+6\le 0 \\ 2x^{2}+5x+2>0 \\ x^{2}-2x-1<0 \end{array} \Leftrightarrow \begin{array}{|l} 5(x-2)\left( x+\frac{3}{5} \right)\le 0 \\ 2(x+2)\left(x+\frac{1}{2} \right)>0 \\ (x-1-\sqrt{2})(x-1+\sqrt{2})<0 \end{array}\Rightarrow \end{aligned}[/tex]$$ x \in \left(-\frac{1}{2};0\right) \cup (0;2] $$