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

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

设abc=1,求(a/ab+a+1)+(b/bc+b+1)+(c/ca+c+1)的值 .
因为abc=1,所以 bc=1/a
(a/ab+a+1)+(b/bc+b+1)+(c/ca+c+1)
=[a/(ab+a+1)]+[b/(1/a+b+1)]+[c/(ca+c+abc)]
=a/(ab+a+1)+ab/(1+ab+a)+1/(a+1+ab)
=(a+ab+1)/(ab+a+1)
=1