Dùng tính chất cơ bản của phân thức. Chứng minh rằng: 15x-10 / 3x^2 + 3x - (2x+2)

* Hướng dẫn giải

$\begin{array}{l}\frac{15\mathrm{x}-10}{3{\mathrm{x}}^2+3\mathrm{x}-\left(2\mathrm{x}+2\right)}=\frac{5\left(3\mathrm{x}-2\right)}{3\mathrm{x}\left(\mathrm{x}+1\right)-2\left(\mathrm{x}+1\right)}=\frac{5\left(3\mathrm{x}-2\right)}{\left(3\mathrm{x}-2\right)\left(\mathrm{x}+1\right)}=\frac{5}{\mathrm{x}+1}\\ \frac{5{\mathrm{x}}^2-5\mathrm{x}+5}{{\mathrm{x}}^3+1}=\frac{5\left({\mathrm{x}}^2-\mathrm{x}+1\right)}{\left(\mathrm{x}+1\right)\left({\mathrm{x}}^2-\mathrm{x}+1\right)}=\frac{5}{\mathrm{x}+1}\\ \Rightarrow \frac{15\mathrm{x}-10}{3{\mathrm{x}}^2+3\mathrm{x}-\left(2\mathrm{x}+2\right)}=\frac{5{\mathrm{x}}^2-5\mathrm{x}+5}{{\mathrm{x}}^3+1}\end{array}$