Competition problem — Algebra — Maths Olympiad Prep

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Algebra Difficulty 5.4 AIME, harder Find the answer

Example 1 Let $a, b, c$ be positive real numbers, find
$\frac{a+3 c}{a+2 b+c}+\frac{4 b}{a+b+2 c}-\frac{8 c}{a+b+3 c}$

the minimum value.

Your answer

A number or a short expression. Spacing and $ signs are ignored.

Solution

None

Translate the text above into English, please retain the original text's line breaks and format, and output the translation result directly.

Note: The provided instruction is a meta-instruction and not part of the text to be translated. Since the text to be translated is "None", the translation is also "None". Here is the formatted output as requested:

None

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