若abc=1,求ab+a+1分之a+bc+b+1分之b+a+c+1分之c的值
问题描述：
若abc=1,求ab+a+1分之a+bc+b+1分之b+a+c+1分之c的值
答
a/(ab+a+1)+b/(bc+b+1)+c/(ac+c+1)
=a/(ab+a+abc)+b/(bc+b+1)+c/(ac+c+1)
=1/(b+1+bc)+b/(bc+b+1)+c/(ac+c+1)
=(1+b)/(bc+b+1)+c/(ac+c+1)
=(abc+b)/(bc+b+abc)+c/(ac+c+1)
=(ac+1)/(c+1+ac)+c/(ac+c+1)
=(ac+c+1)/(ac+c+1)=1
答
最后一项写错了,应该是(ca+c+1)分之c. a/(ab+a+1) +b/(bc+b+1) +c/(ca+c+1)=a/(ab+a+abc)+b/(bc+b+1)+c/(ca+c+abc)=1/(b+1+bc)+b/(bc+b+1)+1/(a+ab+1)=1/(b+1+bc)+b/(bc+b+1)+abc/(a+ab+abc)=1/(b+1+bc)+b/(bc+b+1)+...