f(x)=lnx-2(x-1)/(x+1),f'(x)=1/x-[2(x+1)-2(x-1)]/(x+1)^2=1/x-4/(x+1)^2=[(x+1)^2-4x]/[x(x+1)^2]=(x-1)^2/[x(x+1)^2]>0,当x>1时,且f(1)=0,于是f递增,f(x)>f(1)=0,即lnx>2(x-1)/(x+1)