Thực hiện rút gọn các biểu thức: x+1/2x-2 - 2x/x^2-1

* Hướng dẫn giải

$\begin{array}{l}\frac{\mathrm{x}+1}{2\mathrm{x}-2}-\frac{2\mathrm{x}}{{\mathrm{x}}^2-1}=\frac{\mathrm{x}+1}{2(\mathrm{x}-1)}-\frac{2\mathrm{x}}{(\mathrm{x}-1)(\mathrm{x}+1)}=\frac{{\left(\mathrm{x}+1\right)}^2-2\mathrm{x}.2}{2(\mathrm{x}-1)(\mathrm{x}+1)}=\frac{{\mathrm{x}}^2+2\mathrm{x}+1-4\mathrm{x}}{2(\mathrm{x}-1)(\mathrm{x}+1)}\\ =\frac{{\mathrm{x}}^2-2\mathrm{x}+1}{2(\mathrm{x}-1)(\mathrm{x}+1)}=\frac{{\left(\mathrm{x}-1\right)}^2}{2(\mathrm{x}-1)(\mathrm{x}+1)}=\frac{\mathrm{x}-1}{2(\mathrm{x}+1)}\end{array}$