若a,.b,c均大于0,且abc=1,则a/ab+a+1+b/bc+b+1+c/ca+c+1=
问题描述：
若a,.b,c均大于0,且abc=1,则a/ab+a+1+b/bc+b+1+c/ca+c+1=
答
abc=1
所以ab=1/c
bc=1/a
b=1/ac
所以
a/ab+a+1+b/bc+b+1+c/ca+c+1
=a/(1/c+a+1)+(1/ac)/(1/a+1/ac+1)+c/(ac+c+1)
=ac/(ac+c+1)+1/(ac+c+1)+c/(ac+c+1)
=(ac+c+1)/(ac+c+1)
=1