giải bất phương trình 1/(x-2)-(1/x)-2/(x+2)<=0

Đáp án:

$\begin{array}{l}
\frac{1}{{x – 2}} – \frac{1}{x} – \frac{2}{{x + 2}} \le 0\\
 \Rightarrow \frac{{x\left( {x + 2} \right) – \left( {x – 2} \right)\left( {x + 2} \right) – 2x\left( {x – 2} \right)}}{{x\left( {x + 2} \right)\left( {x – 2} \right)}} \le 0\\
 \Rightarrow \frac{{{x^2} + 2x – {x^2} + 4 – 2{x^2} + 4x}}{{x\left( {x + 2} \right)\left( {x – 2} \right)}} \le 0\\
 \Rightarrow \frac{{3x + 2}}{{x\left( {x + 2} \right)\left( {x – 2} \right)}} \le 0\\
 \Rightarrow \left[ \begin{array}{l}
\left\{ \begin{array}{l}
3x + 2 \le 0\\
x\left( {{x^2} – 4} \right) > 0
\end{array} \right.\\
\left\{ \begin{array}{l}
3x + 2 \ge 0\\
x\left( {{x^2} – 4} \right) < 0
\end{array} \right.
\end{array} \right.\\
 \Rightarrow \left[ \begin{array}{l}
 – 2 < x \le  – \frac{2}{3}\\
0 < x < 2
\end{array} \right.
\end{array}$