How do I simplify (1-x)/(x-1)?

1. Factor out a (-1) from the numerator.
              -(-1+x)/(x-1)
2. You can now simplify the fraction,
            -(+x-1)/(+x-1)
              -1/1  (the x-1 is same for both the numerator and denominator, so they can be canceled out)
              =-1   
which brings you to your answer (-1).