Thu gọn ​\(A=\frac{3 x^{3}-7 x^{2}+5 x-1}{2 x^{3}-x^{2}-4 x+3}\) ta được

* Hướng dẫn giải

Ta có:

\(\begin{aligned} &A=\frac{3 x^{3}-3 x^{2}-4 x^{2}+4 x+x-1}{2 x^{3}-2 x^{2}+x^{2}-x-3 x+3} \\ &A=\frac{3 x^{2}(x-1)-4 x(x-1)+(x-1)}{2 x^{2}(x-1)+x(x-1)-3(x-1)} \\ &A=\frac{(x-1)\left(3 x^{2}-4 x+1\right)}{(x-1)\left(2 x^{2}+x-3\right)}=\frac{(x-1)(x-1)(3 x-1)}{(x-1)(2 x+3)(x-1)} \\ &A=\frac{(x-1)^{2}(3 x-1)}{(x-1)^{2}(2 x+3)}=\frac{3 x-1}{2 x+3} \end{aligned}\)