i presume this is
y = x/(x-1) + 1/(1-x)
Multiply last term by -1/-1 in order to give the expressions a common denominator.
y = x/(x-1) - 1/(x-1)
Combine the expressions, since they now have a common denominator
y = (x-1)/(x-1)
y = 1 except that the function is undefined when x = 1, because that would mean you were dividing by zero.