若B+1/C=1,C+A/1=1,求AB+1/B的值设ABC=1,则A/(AB+A+1)+B/(BC+B+1)+C/(CA+C+1)的值

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若B+1/C=1,C+A/1=1,求AB+1/B的值设ABC=1,则A/(AB+A+1)+B/(BC+B+1)+C/(CA+C+1)的值若B+1/C=1,C+A/1=1,求AB+1/B的值设ABC=1

若B+1/C=1,C+A/1=1,求AB+1/B的值设ABC=1,则A/(AB+A+1)+B/(BC+B+1)+C/(CA+C+1)的值
若B+1/C=1,C+A/1=1,求AB+1/B的值
设ABC=1,则A/(AB+A+1)+B/(BC+B+1)+C/(CA+C+1)的值

若B+1/C=1,C+A/1=1,求AB+1/B的值设ABC=1,则A/(AB+A+1)+B/(BC+B+1)+C/(CA+C+1)的值
1.由b+1/c=1,得:b=1-1/c=(c-1)/c,则1/b=c/(c-1),
由c+1/a=1,得:1/a=1-c,则a=1/(1-c),
所以
a+1/b
=1/(1-c)+c/(c-1)
=1/(1-c)-c/(1-c)
=(1-c)/(1-c)
=1
2.因为 1=abc
所以a/(ab+a+1)+b/(bc+b+1)+c/(ca+c+1)
=a/(ab+a+abc)+b/(bc+b+1)+c/(ca+c+1)
=1/(bc+b+1)+b/(bc+b+1)+c/(ca+c+1)
=(1+b)/(bc+b+1)+c/(ca+c+1)(前2项通分相加)
=(1+b)/(bc+b+abc)+c/(ca+c+1)
=(1+b)/b(c+1+ac)+c/(ca+c+1)
=(1+b+bc)/b(c+1+ac)
=(abc+b+bc)/b(c+1+ac)
=b(ac+1+c)/b(c+1+ac)
=1