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