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abc=1,求,ab+a+1分之a+bc+b+1分之b+ac+c+1分之c的值
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abc=1,求,ab+a+1分之a+bc+b+1分之b+ac+c+1分之c的值
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答案和解析
1=abc
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/(bc+b+1) + 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+1)/(ac+c+1) + c/(ac+c+1)
= (ac+1+c)/(ac+c+1)
= 1
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/(bc+b+1) + 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+1)/(ac+c+1) + c/(ac+c+1)
= (ac+1+c)/(ac+c+1)
= 1
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