Cộng, trừ các phân thức sau: x^3 + x^2 -2x-20/x^2 -4 -5/x+2 + 3/x-2

* Hướng dẫn giải

$\begin{array}{l}\frac{{\mathrm{x}}^3+{\mathrm{x}}^2-2\mathrm{x}-20}{{\mathrm{x}}^2-4}-\frac{5}{\mathrm{x}+2}+\frac{3}{\mathrm{x}-2}\\ =\frac{{\mathrm{x}}^3+{\mathrm{x}}^2-2\mathrm{x}-20-5\left(\mathrm{x}-2\right)+3\left(\mathrm{x}+2\right)}{\left(\mathrm{x}-2\right)\left(\mathrm{x}+2\right)}\\ =\frac{{\mathrm{x}}^3+{\mathrm{x}}^2-4\mathrm{x}-4}{\left(\mathrm{x}-2\right)\left(\mathrm{x}+2\right)}=\frac{\left(\mathrm{x}+1\right)\left({\mathrm{x}}^2-4\right)}{{\mathrm{x}}^2-4}=\mathrm{x}+1\end{array}$