x/x-1减去2x-2/x减去1=0
x/(x-1) - (2x-2)/x -1 = 0
两边同时乘以 x(x-1),得
x^2 - 2(x-1)^2 - x(x-1) =0
(x+(x-1))(x-2(x-1)) = 0
即 (2x-1)(1-x) = 0
得 2x-1 = 0 或 1-x =0
即 x = 1/2,x=1
经验算, x=1不成立,所以方程的根是 x = 1/2