Let $a$ and $b$ be real numbers such that $a > b > 0.$  Determine the minimum value of
\[a + \frac{1}{b(a - b)}.\]
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Let $a$ and $b$ be real numbers such that $a > b > 0.$  Determine the minimum value of
\[a + \frac{1}{b(a - b)}.\]
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

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