已知abc不等于0,且a+b+c=0,求a(1/b+1/c)+b(1/c+1/a)+c(1/a+1/b)的值

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已知abc不等于0,且a+b+c=0,求a(1/b+1/c)+b(1/c+1/a)+c(1/a+1/b)的值

已知abc不等于0,且a+b+c=0,求a(1/b+1/c)+b(1/c+1/a)+c(1/a+1/b)的值
已知abc不等于0,且a+b+c=0,求a(1/b+1/c)+b(1/c+1/a)+c(1/a+1/b)的值

已知abc不等于0,且a+b+c=0,求a(1/b+1/c)+b(1/c+1/a)+c(1/a+1/b)的值
a(1/b+1/c)+b(1/c+1/a)+c(1/a+1/b)=(a+c)/b+(a+b)/c+(b+c)/a
=(a+c)/b+1+(a+b)/c+1+(b+c)/a+1-3
=(a+c+b)/b+(a+b+c)/c+(b+c+a)/a-3=0+0+0-3=-3

a(1/b+1/c)+b(1/a+1/
c)+c(1/a+1/b)
=(a+b)/c+(b+c)/a+(c+a)/b
=(-c)/c+(-a)/a+(-b)/b
=-3

原式
=a/b+a/c+b/c+b/a+c/a+c/b
=(b+c)/a+(a+c)/b+(a+b)/c
=(-a)/a+(-b)/b+(-c)/c
=-1-1-1
=-3