\(ĐK:x\ne1\)
\(\Leftrightarrow\dfrac{1}{x-1}-\dfrac{3x^2}{\left(x-1\right)\left(x^2+x+1\right)}-\dfrac{2x}{x^2+x+1}=0\)
\(\Leftrightarrow\dfrac{\left(x^2+x+1\right)-3x^2-2x\left(x-1\right)}{\left(x-1\right)\left(x^2+x+1\right)}=0\)
\(\Leftrightarrow x^2+x+1-3x^2-2x^2+2x=0\)
\(\Leftrightarrow-4x^2+3x+1=0\)
\(\Leftrightarrow\left(x-1\right)\left(x+\dfrac{1}{4}\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=1\left(ktm\right)\\x=-\dfrac{1}{4}\left(tm\right)\end{matrix}\right.\)
ĐKXĐ: \(x\ne1\)
\(\dfrac{x^2+x+1}{\left(x-1\right)\left(x^2+x+1\right)}-\dfrac{3x^2}{\left(x-1\right)\left(x^2+x+1\right)}=\dfrac{2x\left(x-1\right)}{\left(x-1\right)\left(x^2+x+1\right)}\)
\(\Rightarrow x^2+x+1-3x^2=2x\left(x-1\right)\)
\(\Leftrightarrow-2x^2+x+1=2x^2-2x\)
\(\Leftrightarrow4x^2-3x-1=0\)
\(\Rightarrow\left[{}\begin{matrix}x=1\left(loại\right)\\x=-\dfrac{1}{4}\end{matrix}\right.\)
