Let $x > y > z > 0$ be real numbers.  Find the minimum value of
\[x + \frac{108}{(x - y)^3 (y - z)^2 z}.\]
Question:
Let $x > y > z > 0$ be real numbers.  Find the minimum value of
\[x + \frac{108}{(x - y)^3 (y - z)^2 z}.\]
Answer:
Let's think step by step.

user
7
Let $x > y > z > 0$ be real numbers.  Find the minimum value of
\[x + \frac{108}{(x - y)^3 (y - z)^2 z}.\]
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