abc不等于0,计算a{1/b+1/c}+b{1/c+1/a}+c{1/a+1/b}+3的值,1
问题描述：
abc不等于0,计算a{1/b+1/c}+b{1/c+1/a}+c{1/a+1/b}+3的值,
1
答
差条件,
abc不等于0,且a+b+c=0
计算a{1/b+1/c}+b{1/c+1/a}+c{1/a+1/b}+3的值,
abc不等于0,且a+b+c=0
所以
a{1/b+1/c}+b{1/c+1/a}+c{1/a+1/b}+3
=a/b+a/c+b/c+b/a+c/a+c/b+3
=(a/b+c/b)+(a/c+b/c)+(b/a+c/a)+3
=(a+c)/b+(a+b)/c+(b+c)/a+3
=-b/b-c/c-a/a+3
=-1-1-1+3
=0