The number of roots of the equation  $x-\frac{2}{x-1}=1-\frac{2}{x-1}$ , is 

The given equation is meaningful for $x \ne 1$

Now , $x-\frac{2}{x-1}=1-\frac{2}{x-1}\Rightarrow x=1$

But, the equation exists for $x \ne 1$.

Hence, the equation has no solution.