Let $a$ and $b$ be real numbers such that $a > b > 0.$  Determine the minimum value of
\[a + \frac{1}{b(a - b)}.\]
Question:
Let $a$ and $b$ be real numbers such that $a > b > 0.$  Determine the minimum value of
\[a + \frac{1}{b(a - b)}.\]
Answer:
Let's think step by step.

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3
Let $a$ and $b$ be real numbers such that $a > b > 0.$  Determine the minimum value of
\[a + \frac{1}{b(a - b)}.\]
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