求极限化简啊...lim x=>1+ x/(x-1)-1/ln(x)

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求极限化简啊...lim x=>1+ x/(x-1)-1/ln(x)
求极限化简啊...
lim x=>1+ x/(x-1)-1/ln(x)

求极限化简啊...lim x=>1+ x/(x-1)-1/ln(x)
lim x=>1+ x/(x-1)-1/ln(x)
=lim x=>1+(xlnx-(x-1))/(x-1)lnx 0/0的形式,应用罗必塔法则
=lim x=>1+(lnx+x*1/x-1)/(lnx+(x-1)/x)
=lim x=>1+ lnx/(lnx+1-1/x) 也是0/0的形式,继续
=lim x=>1+ 1/x / (1/x+1+1/x^2)
=lim x=>1+ x /(x+x^2+1)
=1/(1+1+1)
=1/3