x>1/1-x
x(1-x)/(1-x)>1/(1-x)
x(1-x)/(1-x)-1/(1-x)>0
(x-x²-1)/(1-x)>0
(x²-x+1)/(x-1)>0
x²-x+1=(x-1/2)²+3/4>0
∴x-1>0
x>1(x-x²-1)/(1-x)>0 变成 (x²-x+1)/(x-1)>0不等号不变么？………………分子，分母同时变，所以不变号