Cộng các phân thức sau: x^2 + 2/ x^3 - 1 + 2/x^2 + x +1

* Hướng dẫn giải

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