若a+x*x=1991 b+x*x=1992 c+x*x=1993 且abc=24 a/bc + b/ca + c/ab - 1/a - 1/b - 1/c 的值

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若a+x*x=1991 b+x*x=1992 c+x*x=1993 且abc=24 a/bc + b/ca + c/ab - 1/a - 1/b - 1/c 的值
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若a+x*x=1991 b+x*x=1992 c+x*x=1993 且abc=24 a/bc + b/ca + c/ab - 1/a - 1/b - 1/c 的值
若a+x*x=1991 b+x*x=1992 c+x*x=1993 且abc=24 a/bc + b/ca + c/ab - 1/a - 1/b - 1/c 的值

若a+x*x=1991 b+x*x=1992 c+x*x=1993 且abc=24 a/bc + b/ca + c/ab - 1/a - 1/b - 1/c 的值
答案为1/8.
b-a=1,c-a=2,c-b=1.
a/bc + b/ca + c/ab - 1/a - 1/b - 1/c
=a/bc + b/ca + c/ab -b/ab-c/bc-a/ca
=a/bc-c/bc+b/ca-a/ca+c/ab-b/ab
=(a-c)/bc+(b-a)/ca+(c-b)/ab
=(a(a-c)+b(b-c)+c(c-b))/abc
=(-2a+b+c)/abc
=(b-a+c-a)/abc
=1/8