Giải bất phương trình x/ x-2 - 2 / x + 1 lớn hơn bằng 1

ĐKXĐ: \[\left\{ \begin{array}{l}x - 2 \ne 0\\x + 1 \ne 0\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}x \ne 2\\x \ne  - 1\end{array} \right.\].

Ta có:

\[\frac{x}{{x - 2}} - \frac{2}{{x + 1}} \ge 1 \Leftrightarrow \frac{{{x^2} + x - 2x + 4}}{{\left( {x - 2} \right)\left( {x + 1} \right)}} - \frac{{(x - 2)(x + 1)}}{{(x - 2)(x + 1)}} \ge 0\]

\[ \Leftrightarrow \frac{{{x^2} - x + 4 - {x^2} + x + 2}}{{\left( {x - 2} \right)\left( {x + 1} \right)}} \ge 0 \Leftrightarrow \frac{6}{{\left( {x - 2} \right)\left( {x + 1} \right)}} \ge 0 \Leftrightarrow {x^2} - x - 2 > 0\]

\[ \Leftrightarrow \left[ \begin{array}{l}x <  - 1\\x > 2\end{array} \right.\].