Radical Fractions, Man!

Algebra Level 4

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 $a + b$ ?