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

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

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

已知a+b+c=0,且abc不等于0,化简a(1/b+1/c)0+b(1/c+1/a)+c(1/a+1/b)
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+a/c+b/c+b/a+c/a+c/b+1+1+1-3
=a/c+b/c+1+a/b+c/b+1+b/a+c/a+1-3
=a/c+b/c+c/c+a/b+c/b+b/b+b/a+c/a+c/c-3
=[(a+b)/c+c/c]+[(a+c)/b+b/b]+[(b+c)/a+a/a] -3
=(a+b+c)/c+(a+b+c)/b+(a+b+c)/a -3
=0+0+0-3
=-3

-3
将a+b=-c带入即可、