abc=1,
则ab=1/c,ac=1/b,bc=1/a
a/(ab+a+1)
=a/(1/c+a+1)
=ac/(1+ac+c)…………（分子分母同时乘c）
a/(ab+a+1)+c/(ac+c+1)
=(ac+c)/(ac+c+1)
=(1/b+c)/(1/b+c+1)
=(1+bc)/(1+bc+b)…………（分子分母同时乘b）
a/(ab+a+1)+b/(bc+b+1)+c/(ac+c+1)
=(1+bc)/(bc+b+1)+b/(bc+b+1)
=(bc+b+1)/(bc+b+1)
=1