a/(ab+a+1)+b/(bc+b+1)+c/(ac+c+1)
=ac/(abc+ac+c)+1/(c+1+1/b)+c/(ac+c+1)
=ac/(1+ac+c)+1/(c+1+ac)+c/(ac+c+1)
=(ac+1+c)/(1+ac+c)
=1
a/(ab+a+1)+b/(bc+b+1)+c/(ac+c+1)
=ac/(abc+ac+c)+1/(c+1+1/b)+c/(ac+c+1)
=ac/(1+ac+c)+1/(c+1+ac)+c/(ac+c+1)
=(ac+1+c)/(1+ac+c)
=1