解:∵a·b=1
∴M=a/﹙a+1﹚+b/﹙b+1﹚
=a/﹙a+ab﹚+b/﹙b+ab﹚
=a/a﹙b+1﹚+b/b﹙a+1﹚
=1/﹙a+1﹚+1/﹙b+1﹚
=N
∴ M=N.
或M - N = a/(a + 1)+ b/(b + 1)- 1/(a + 1)- 1/(b + 1)
=(a - 1)/(a + 1)+ (b - 1)/(b + 1)
=(ab + a - b - 1 + ab - a + b - 1)/(a + 1)(b + 1)
=(2ab - 2)/(ab + a + b + 1)
= 0 ------------------分子为0
所以M = N
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