Radical Fractions, Man!

Algebra Level 3

The expression \( \frac {1}{ 1 \sqrt{2} + 2 \sqrt{1} }+ \frac {1}{ 2 \sqrt{3} + 3 \sqrt{2} } + \ldots + \frac {1} { 9999 \sqrt{10000} + 10000 \sqrt{9999} } \) is equal to \( \frac { a}{b} \), where \(a\) and \(b\) are coprime positive integers. What is \( a + b \)?

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