若ab=1,则a/(a+1)+b/(b+1)=?

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若ab=1,则a/(a+1)+b/(b+1)=?

若ab=1,则a/(a+1)+b/(b+1)=?
若ab=1,则a/(a+1)+b/(b+1)=?

若ab=1,则a/(a+1)+b/(b+1)=?
因为ab=1
所以:
a/(a+1)+b/(b+1)
=a/(a+ab)+b/(b+1)
=1/(1+b)+b/(b+1)
=(1+b)/(b+1)
=1
故:a/(a+1)+b/(b+1)=1

1
a=1/b
(1/b)/{(1/b)+1)}+b/(b+1)
=1/(b+1)+b/(b+1)
=1

先通分a/(a+1)+b/(b+1)=(ab+a+ab+b)/(a+1)(b+1)
=(a+b+2ab)/(ab+a+b+1)
而ab=1,代入上式
∴原式=1

原式=[a(b+1)+b(a+1)]/(a+1)(b+1)
=(ab+a+ab+b)/(ab+a+b+1)
=(a+b+2)/(a+b+2)
=1