Compute
\[\sum_{n = 2}^{10000} \frac{1}{n \sqrt{n - 1} + (n - 1) \sqrt{n}}.\]The answer is in the form rac{m}{n}, where gcd(m, n) = 1. Please provide the value of m + n.

Let's think step by step and output the final answer within \boxed{}.
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