ab/(a+b) = 1/3,左边分子分母同除以ab得:1/(1/a+1/b) =1/3,则
1/a + 1/b = 3
同理,有:
1/(1/b + 1/c) = 4
1/(1/a + 1/c) = 5
以上三式相加,得 :2(1/a+1/b+1/c) = 12
所以,1/a+1/b+1/c = 6