To solve the problem, we follow these key steps:

Step 1: Use (a+b+c=0) to simplify each denominator

Given (a+b+c=0), we can rewrite (a = -(b+c)). Squaring both sides:
(a^2 = (b+c)^2 = b^2 + 2bc + c^2).

Thus:
(b^2 + c^2 - a^2 = b^2 + c^2 - (b^2 + 2bc + c^2) = -2bc).

Similarly:
(a^2 + c^2 - b^2 = -2ac)
(a^2 + b^2 - c^2 = -2ab)

Step 2: Substitute into the expression

The original expression becomes:
[ \frac{1}{-2bc} + \frac{1}{-2ac} + \frac{1}{-2ab} = -\frac{1}{2}\left(\frac{1}{bc} + \frac{1}{ac} + \frac{1}{ab}\right) ]

Combine the fractions inside the parentheses:
[ \frac{a + b + c}{abc} ]

Since (a+b+c=0), this numerator is zero.

Final Result

The entire expression equals (-\frac{1}{2} \times 0 = 0).

Answer: A (assuming option A is 0)

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作者声明:本文包含人工智能生成内容。