已知abc=1,求证a/ab+a+1+a/bc+b+1+c/ac+c+1=1是求证,,,
问题描述：
已知abc=1,求证a/ab+a+1+a/bc+b+1+c/ac+c+1=1
是求证,,,
答
a/(ab+a+1)=a/(ab+a+abc)=1/(b+1+bc)
b/(bc+b+1)=b/(b+1+bc)
c/(ac+c+1)=abc/(a^2bc+abc+ab)=bc/(abc+bc+b)=bc/(1+bc+b)
三式相加
a/(ab+a+1)+b/(bc+b+1)+c/(ac+c+1)=(1+b+bc)/(1+b+bc)=1
答
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