ĐKXĐ: ...
\(\Leftrightarrow x^3+\frac{x^3}{\left(x-1\right)^3}+3x.\frac{x}{x-1}\left(x+\frac{x}{x-1}\right)-\frac{3x^2}{\left(x-1\right)}\left(x+\frac{x}{x-1}\right)+\frac{3x^2}{x-1}-2=0\)
\(\Leftrightarrow\left(x+\frac{x}{x-1}\right)^3-3\left(\frac{x^2}{x-1}\right)^2+3\left(\frac{x^2}{x-1}\right)-1-1=0\)
\(\Leftrightarrow\left(\frac{x^2}{x-1}\right)^3-3\left(\frac{x^2}{x-1}\right)^2+3\left(\frac{x^2}{x-1}\right)-1-1=0\)
\(\Leftrightarrow\left(\frac{x^2}{x-1}-1\right)^3-1=0\)
\(\Leftrightarrow\frac{x^2}{x-1}-1=1\)
\(\Leftrightarrow x^2-2x+2=0\)
Phương trình vô nghiệm