解法二.
abc/(ab+bc+ac)=1/6.
因为ab/(a+b)=1/3
==>(a+b)/ab=3
==>1/a+1/b=3
同理:1/b+1/c=4,1/a+1/c=5.
而(ab+bc+ac)/abc
=1/a+1/b+1/c
=(3+4+5)/2
=6
所以abc/(ab+bc+ac)=1/6.
解法一.
ab/(a+b)=1/3,
(a+b)/ab=3,
1/b+1/a=3
bc/(b+c)=1/4,
(b+c)/bc=4,
1/c+1/b=4
ac/(a+c)=1/5,
(a+c)/ac=5,
1/c+1/a=5
1/a+1/a+1/b+1/b+1/c+1/c=12
2/a+2/b+2/c=12
(2bc+2ac+2ab)/abc=12
(bc+ac+ab)/abc=6
所以ab+bc+ac分之abc=1/6