已知abc=1,求ab+a+1/a+bc+b+1/b+ac+c+1/c的值

已知abc=1,求ab+a+1/a+bc+b+1/b+ac+c+1/c的值
已知abc=1,求ab+a+1/a+bc+b+1/b+ac+c+1/c的值

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

等于九