Rút gọn biểu thức: A = (9/ x^3 -9x + 1/x+3) : (x-3/x^2 + 3x - x/3x+9)

* Hướng dẫn giải

$\begin{array}{l}\mathrm{A}=\left(\frac{9}{{\mathrm{x}}^3-9\mathrm{x}}+\frac{1}{\mathrm{x}+3}\right):\frac{{\mathrm{x}}^2+3\mathrm{x}}{1-3\mathrm{x}}\\ =\left[\frac{9}{\mathrm{x}\left({\mathrm{x}}^2-9\right)}+\frac{1}{\mathrm{x}+3}\right]:\frac{\mathrm{x}\left(\mathrm{x}+3\right)}{1-3\mathrm{x}}=\frac{9+\mathrm{x}\left(\mathrm{x}-3\right)}{\mathrm{x}\left(\mathrm{x}-3\right)\left(\mathrm{x}+3\right)}.\frac{1-3\mathrm{x}}{\mathrm{x}\left(\mathrm{x}+3\right)}\\ =\frac{\left({\mathrm{x}}^2+3\mathrm{x}+9\right).\left(1-3\mathrm{x}\right)}{{\left(\mathrm{x}+3\right)}^2.\left(\mathrm{x}-3\right){\mathrm{x}}^2}\end{array}$