已知abc=1,求a/(ab+a+1)+b/(bc+b+1)+c/(ac+c+1)的值(麻烦用文字叙述)

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已知abc=1,求a/(ab+a+1)+b/(bc+b+1)+c/(ac+c+1)的值(麻烦用文字叙述)

a/(ab+a+1)=ac/(abc+ac+c)=ac/(ac+c+1)
b/(bc+b+1)=abc/(abc²+abc+ac)=1/(c+1+ac)
a/(ab+a+1)+b/(bc+b+1)+c/(ac+c+1)
=ac/(ac+c+1)+1/(ac+c+1)+c/(ac+c+1)
=(ac+c+1)/(ac+c+1)
=1