解法1：
[ln(x+1)-lnx]'
=[ln(x+1)]'-(lnx)'
=1/(x+1)-1/x
=x/[x(x+1)]-(x+1)/[x(x+1)]
=[x-(x+1)]/[x(x+1)]
=(x-x-1)/[x(x+1)]
=-1/[x(x+1)]