x1>x2>1
f(x1)-f(x2)
=-2/(x1-1)+2/(x2-1)
=2(x1-1-x2+1)/(x1-1)(x2-1)
=2(x1-x2)/(x1-1)(x2-1)
x1>x2则分子大于0
x1>1,x2>2,所以分母大于0
所以f(x1)-f(x2)>0
即x1>x2>1时有f(x1)>f(x2)
所以是增函数
x1>x2>1
f(x1)-f(x2)
=-2/(x1-1)+2/(x2-1)
=2(x1-1-x2+1)/(x1-1)(x2-1)
=2(x1-x2)/(x1-1)(x2-1)
x1>x2则分子大于0
x1>1,x2>2,所以分母大于0
所以f(x1)-f(x2)>0
即x1>x2>1时有f(x1)>f(x2)
所以是增函数