ĐKXĐ:...
\(\Leftrightarrow x^2-2x-1+2\left(x-1\right)\sqrt{x^2+2x-1}=0\)
\(\Leftrightarrow x^2+2x-5+2\left(x-1\right)\sqrt{x^2+2x-1}-4\left(x-1\right)=0\)
\(\Leftrightarrow x^2+2x-5+2\left(x-1\right)\left[\sqrt{x^2+2x-1}-2\right]=0\)
\(\Leftrightarrow x^2+2x-5+\frac{2\left(x-1\right)\left(x^2+2x-5\right)}{\sqrt{x^2+2x-1}+2}=0\)
\(\Leftrightarrow\left(x^2+2x-5\right)\left[1+\frac{2x-2}{\sqrt{x^2+2x-1}+2}\right]=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x^2+2x-5=0\\1=\frac{2-2x}{\sqrt{x^2+2x-1}+2}\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x^2+2x-5=0\\\sqrt{x^2+2x-1}=-2x\left(x\le0\right)\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x^2+2x-5=0\\3x^2-2x+1=0\end{matrix}\right.\) \(\Leftrightarrow...\)