$The equation x-\frac{ 2}{x-1}=1-\frac{2}{x-1} has$

$$\begin{gathered} x-\frac{2}{x-1}=1-\frac{2}{x-1} \\ \frac{x^2-x-2}{x-1}=\frac{x-1-2}{x-1} \\ {x}^2-x-2=x-1-2 \\ {x}^2-x-2-x+3=0 \\ {x}^2-2x+1=0 \\ {(x-1)}^2=0 x=1,1 \\ If x=1 the given question does not exist \end{gathered}$$