∵ab=1
∴a/(a+1)+b/(b+1)
=1-1/(a+1)+1-1/(b+1)
=2-[1/(a+1)+1/(b+1)]
=2-[(a+1+b+1)/(a+1)(b+1)]
=2-[(a+b+2)/(ab+a+b+1)]
=2-[(a+b+2)/(a+b+2)]
=2-1
=1