ĐKXĐ: \(x\ne1;x\ne\dfrac{1}{3}\)
\(\dfrac{2x}{3x^2-x+1}-\dfrac{1}{2}+\dfrac{x}{3x^2-4x+1}-1=0\)
\(\Leftrightarrow\dfrac{-3x^2+5x-1}{6x^2-2x-2}+\dfrac{-3x^2+5x-1}{3x^2-4x+1}=0\)
\(\Leftrightarrow\left(-3x^2+5x-1\right)\left(\dfrac{1}{6x^2-2x-2}+\dfrac{1}{3x^2-4x+1}\right)=0\)
TH1: \(-3x^2+5x-1=0\Rightarrow\left[{}\begin{matrix}x=\dfrac{5-\sqrt{13}}{6}\\x=\dfrac{5+\sqrt{13}}{6}\end{matrix}\right.\)
TH2: \(\dfrac{1}{6x^2-2x-2}+\dfrac{1}{3x^2-4x+1}=0\Leftrightarrow\dfrac{9x^2-6x-1}{\left(6x^2-2x-2\right)\left(3x^2-4x+1\right)}=0\)
\(\Leftrightarrow9x^2-6x-1=0\Rightarrow\left[{}\begin{matrix}x=\dfrac{1-\sqrt{2}}{3}\\x=\dfrac{1+\sqrt{2}}{3}\end{matrix}\right.\)
Vậy pt đã cho có 4 nghiệm x=....
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