Thực hiện nhân, chia các phép tính: 4x^2 - 3x +17/ x^3 -1 + 2x-1/ x^2 + x +1 + 6x/x - x^2

* Hướng dẫn giải

$\begin{array}{l}\frac{4{\mathrm{x}}^2-3\mathrm{x}+17}{{\mathrm{x}}^3-1}+\frac{2\mathrm{x}-1}{{\mathrm{x}}^2+\mathrm{x}+1}+\frac{6\mathrm{x}}{\mathrm{x}-{\mathrm{x}}^2}\\ =\frac{4{\mathrm{x}}^2-3\mathrm{x}+17+2{\mathrm{x}}^2-3\mathrm{x}+1}{\left(\mathrm{x}-1\right)\left({\mathrm{x}}^2+\mathrm{x}+1\right)}+\frac{6}{1-\mathrm{x}}\\ =\frac{6{\mathrm{x}}^2-6\mathrm{x}+18}{\left(\mathrm{x}-1\right)\left({\mathrm{x}}^2+\mathrm{x}+1\right)}-\frac{6\left({\mathrm{x}}^2+\mathrm{x}+1\right)}{\left(\mathrm{x}-1\right)\left({\mathrm{x}}^2+\mathrm{x}+1\right)}=\frac{-12\mathrm{x}+12}{\left(\mathrm{x}-1\right)\left({\mathrm{x}}^2+\mathrm{x}+1\right)}\\ =\frac{-12\left(\mathrm{x}-1\right)}{\left(\mathrm{x}-1\right)\left({\mathrm{x}}^2+\mathrm{x}+1\right)}=\frac{-12}{{\mathrm{x}}^2+\mathrm{x}+1}\end{array}$