Question

已知a+b+c=0.怎样能尽快求出a(1/b+1/c)+b(1/c+1/a+)de结果呢啊

Answer 1

a+b+c=0

所以

a+b=-c

a+c=-b

b+c=-a

a(1/b+1/c)+b(1/c+1/a)+c(1/a+1/b)

=a/b+a/c+b/c+b/a+c/a+c/b

=(a+b)/c+(b+c)/a+(c+a)/b

=-c/c+(-a/a)+(-b/b)

=-1-1-1

=-3