Giải phương trình chứa ẩn ở mẫu sau : 2x - 1/x + 1 + 3x - 1/x + 2 = x - 7/x - 1 + 4

* Hướng dẫn giải

$\begin{array}{l}\frac{2x-1}{x+1}+\frac{3x-1}{x+2}=\frac{x-7}{x-1}+4\left(\begin{array}{l}x\ne \pm 1\\ x\ne -2\end{array}\right)\\ \iff \frac{\left(2x-1\right)\left(x+2\right)\left(x-1\right)+\left(3x-1\right)\left(x^2-1\right)}{\left(x+1\right)\left(x-1\right)\left(x+2\right)}=\frac{\left(x-7\right)\left(x+1\right)+4\left(x+2\right)\left(x^2-1\right)}{\left(x+1\right)\left(x-1\right)\left(x+2\right)}\\ \Rightarrow \left(2x^2+3x-2\right)\left(x-1\right)+3x^3-x^2-3x+1=\left(x^2-6x-7\right)\left(x-2\right)+4\left(x^3+2x^2-x-2\right)\\ \iff 2x^3+x^2-5x+2+3x^3-x^2-3x+1=x^3-8x^2+5x+14+4x^3+8x^2-4x-8\\ \iff -9x=-3\iff x=\frac{1}{3}\left(tm\right)\end{array}$