Thực hiện nhân, chia các phép tính: (x^2 + 4x^2 /x^2 -4)

* Hướng dẫn giải

$\begin{array}{l}\left({\mathrm{x}}^2+\frac{4{\mathrm{x}}^2}{{\mathrm{x}}^2-4}\right).\left(\frac{\mathrm{x}+2}{2\mathrm{x}-4}+\frac{2-3\mathrm{x}}{{\mathrm{x}}^3-4\mathrm{x}}.\frac{{\mathrm{x}}^2-4}{\mathrm{x}-2}\right)\\ =\frac{{\mathrm{x}}^4-4{\mathrm{x}}^2+4{\mathrm{x}}^2}{\left(\mathrm{x}+2\right)\left(\mathrm{x}-2\right)}.\left(\frac{\mathrm{x}+2}{2\left(\mathrm{x}-2\right)}+\frac{2-3\mathrm{x}}{\mathrm{x}\left(\mathrm{x}-2\right)}\right)\\ =\frac{{\mathrm{x}}^4}{\left(\mathrm{x}+2\right)\left(\mathrm{x}-2\right)}.\frac{{\mathrm{x}}^2+2\mathrm{x}+4-6\mathrm{x}}{2\mathrm{x}\left(\mathrm{x}-2\right)}=\frac{{\mathrm{x}}^3.{\left(\mathrm{x}-2\right)}^2}{2.(\mathrm{x}+2)\left(\mathrm{x}-2\right)}=\frac{{\mathrm{x}}^3.\left(\mathrm{x}-2\right)}{2\left(\mathrm{x}+2\right)}\end{array}$