已知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a+b+c=0,求a(1/b+1/c)+b(1/c+1/a)+c(1/a+1/b)的值解: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=[(b/a+c/a)+1]+[(a/b+c/b)+1]+[(a/c+b/c)+1]-3=(a+b+c)/a+=(a+b+c)/b+(a+b+c)/c-3=(a+b+c)(1/a+1/b+1/c)-3∵a+b+c=0∴a(1/b+1/c)+b(1/c+1/a)+c(1/a+1/b)=-3