For real numbers $x > 1,$ find the minimum value of
\[\frac{x + 8}{\sqrt{x - 1}}.\]
Question:
For real numbers $x > 1,$ find the minimum value of
\[\frac{x + 8}{\sqrt{x - 1}}.\]
Answer:
Let's think step by step.

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For real numbers $x > 1,$ find the minimum value of
\[\frac{x + 8}{\sqrt{x - 1}}.\]
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