f(x)=x+1/x-1+alnx
f'(x)=1-1/(x-1)^2+a/x
在X=2处取得极值,即有f'(2)=1-1+a/2=0
a=0
f'(x)=1-1/(x-1)^2=(x^2-2x+1-1)/(x-1)^2=x(x-2)/(x-1)^2
又有x>0,故有f'(x)>0时有x>2,即单调增区间是(2,+无穷),在f'(x)