a/(ab+a+1) + b/(bc+b+1) + c/(ca+c+1)
=1/(b+1+1/a) + b/(bc+b+1) + bc/(cab+cb+b)
=1/(b+1+bc) + b/(bc+b+1) + bc/(1+bc+b)
=(b+1+bc)/(b+1+bc)
=1