ĐKXĐ: \(\left[{}\begin{matrix}x>1\\x\le-1\end{matrix}\right.\)
\(\Leftrightarrow\frac{2x+2}{x-1}=x-1\)
\(\Leftrightarrow2x+2=\left(x-1\right)^2\)
\(\Leftrightarrow x^2-4x-1=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=2+\sqrt{5}\\x=2-\sqrt{5}\left(l\right)\end{matrix}\right.\)