Giải phương trình: 1/x-1+1/x-2=1/x+2+1/x+1

* Hướng dẫn giải

$$\begin{gathered} \frac{1}{x-1}+\frac{1}{x-2}=\frac{1}{x+2}+\frac{1}{x+1} \\ \iff \frac{1}{x-1}+\frac{1}{x-2}-\frac{1}{x+2}-\frac{1}{x+1}=0 \\ \iff \left(\frac{1}{x-1}-\frac{1}{x+1}\right)+\left(\frac{1}{x-2}-\frac{1}{x+2}\right)=0 \\ \iff \frac{2}{x^2-1}+\frac{4}{x^2-4}=0 \\ \iff \frac{6x^2-12}{\left(x^2-1\right)\left(x^2-4\right)}=0 \\ \iff 6x^2 - 12 = 0 \iff x = \pm \sqrt{2} \left(TMĐK\right) \end{gathered}$$