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