已知abc=1,求证a/ab+a+1+a/bc+b+1+c/ac+c+1=1

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