已知abc=1,求证：a/(ab+a+1)+b/(bc+a+1)+c/(ca+c+1)=1

题目

已知abc=1,求证：a/(ab+a+1)+b/(bc+a+1)+c/(ca+c+1)=1

答案

题目写错了吧,应该是b/(bc+b+1)啊证明：因为abc=1所以b=1/acab=1/cbc=1/a所以a/(ab+a+1)+b/(bc+b+1)+c/(ca+c+1)=a/(1/c+a+1)+(1/ac)/(1/a+1/ac+1)+c/(ac+c+1)=ac/(ac+c+1)+1/(ac+c+1)+c/(ac+c+1)=(ac+c+1)/(ac+c+1)=...