已知abc=1,求(a/ab+a+1)+(b/bc+b+1)+(ca+c+1)的值.

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已知abc=1,求(a/ab+a+1)+(b/bc+b+1)+(ca+c+1)的值.

已知abc=1,求(a/ab+a+1)+(b/bc+b+1)+(ca+c+1)的值.
已知abc=1,求(a/ab+a+1)+(b/bc+b+1)+(ca+c+1)的值.

已知abc=1,求(a/ab+a+1)+(b/bc+b+1)+(ca+c+1)的值.
你指的是求 a / (ab+a+1)+b /(bc+b+1) + c / (ca+c+1) 的值吗?
使分母里面的 “1” 变成 abc,因为abc=1
则a / (ab+a+1)+b /(bc+b+1) + c / (ca+c+1)
=a / (ab+a+abc) + b/(bc+b+abc) +c / (ca+c+1)
=1/ (bc+b+1) + 1/ (ac+c+1)+c / (ca+c+1)
=abc/(bc+b+abc)+ (c+1)/(ca+c+1) (这里把前面一项的 “1”都变成abc)
=ac /(ca+c+1)+ (c+1)/(ca+c+1)
=1

已知abc=1,求a/(ab+a+1) +b/(bc+b+1) +c/(ca+c+1)的值
a/(ab+a+1)
=a/(ab+a+abc)
=1/(bc+b+1)
a/(ab+a+1)
=(ac)/(abc+ac+c)
=(ac)/(ca+c+1)
进行类似变换可得
3[a/(ab+a+1)+b/(bc+b+1)+c/(ca+c+1...

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已知abc=1,求a/(ab+a+1) +b/(bc+b+1) +c/(ca+c+1)的值
a/(ab+a+1)
=a/(ab+a+abc)
=1/(bc+b+1)
a/(ab+a+1)
=(ac)/(abc+ac+c)
=(ac)/(ca+c+1)
进行类似变换可得
3[a/(ab+a+1)+b/(bc+b+1)+c/(ca+c+1)]
=a/(ab+a+1)+1/(bc+b+1)+(ac)/(ca+c+1)+b/(bc+b+1)+1/(ca+c+1)+(ab)/(ab+a+1)+c/(ca+c+1)+1/(ab+a+1)+(bc)/(bc+b+1)
=(ab+a+1)/(ab+a+1)+(bc+b+1)/(bc+b+1)+(ca+c+1)/(ca+c+1)
=1+1+1
=3
a/(ab+a+1)+b/(bc+b+1)+c/(ca+c+1)=1

收起

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