Tính (2/x+2 - 4/ x^2 + 4x + 4)

* Hướng dẫn giải

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