Giải các phương trình sau : 1/(x-1)-2x^2/(x^3-1)=2x/(x^2+x+1), b. (x-1)/(x+1)-x/(x-2)=(5x-2)/(4-x^2)

* Hướng dẫn giải

$\begin{array}{l}\frac{1}{x-1}-\frac{3x^2}{x^3-1}=\frac{2x}{x^2+x+1}\left(x\ne 1\right)\\ \iff \frac{x^2+x+1-3x^2}{\left(x-1\right)\left(x^2+x+1\right)}=\frac{2x\left(x-1\right)}{\left(x-1\right)\left(x^2+x+1\right)}\\ \Rightarrow -2x^2+x+1=2x^2-2x\iff 4x^2-4x-1=0\\ \iff 4x^2-4x+x-1=0\iff 4x\left(x-1\right)+\left(x-1\right)=0\\ \iff \left(x-1\right)\left(4x+1\right)=0\iff \left[\begin{array}{l}x-1=0\\ 4x+1=0\end{array}\right.\iff \left[\begin{array}{l}x=1\left(ktm\right)\\ x=-\frac{1}{4}\left(tm\right)\end{array}\right.\end{array}$