1/(x-1)=1+x/(x-1)
I hope this is the correct problem
it have no solution which can be proved by 2 methods
1) by inspection x<>1 (otherwise term will become undefined)
multiplying LHS ans RHS by x-1
1=x-1+x or
2x=2
or x=1 but we already know that x<>1 so no solution
2) 1/(x-1)=1+x/(x-1) or
1/(x-1)-[x/(x-1)]=1 or
(1-x)/(x-1)=1 or
-1=1 which is impossible hence no solution

If the problem is, instead, \(\displaystyle 1/(x-1)= (1+x)/(x-1)\), then, as nikhil said, x= 1 cannot be a solution. As long as x is not 1, we can multiply both sides by x-1 to get 1= 1+ x and that has solution x= 0,