已知abc=1,试说明a/(ab+a+1)+b/(bc+b+1)+c/(ca+c+1)=1的理由。
热心网友
a/(ab+a+1)+b/(bc+b+1)+c/(ca+c+1)=a/(ab+a+abc)+b/(bc+b+1)+c/(ca+c+1)=1/(b+1+bc)+b/(bc+b+1)+c/(ca+c+1)=(1+b)/(b+1+bc)+c/(ca+c+1)=(1+b)/(b+1+bc)+c/(ca+c+abc)=(1+b)/(b+abc+bc)+cb/(abc+bc+b)=(1+b+bc)/(b+abc+bc)=(abc+b+bc)/(b+bc+abc)=1
热心网友
a/(ab+a+1)+b/(bc+b+1)+c/(ca+c+1)=a/(ab+a+abc)+b/(bc+b+abc)+c/(ca+c+abc)=1/(b+1+bc)+1/(c+1+ac)+1/(a+1+ab)=abc/(b+abc+bc)+abc/(c+abc+ac)+1/(a+1+ab)=ac/(1+ac+c)+ab/(a+1+ab)+1/(a+1+ab)=ac/(abc+ac+c)+ab/(a+1+ab)+1/(a+1+ab)=a/(ab+a+1)+ab/(a+1+ab)+1/(a+1+ab)=(a+1+ab)/(a+1+ab)=1