Irrational Denominators

Algebra Level 2

\[\frac{1}{ 1 + \sqrt{2} } + \frac{1}{ \sqrt{2} + \sqrt{3} } + \frac{1}{ \sqrt{3} + \sqrt{4} } + \ldots + \frac{1}{ \sqrt{8} + \sqrt{9} } = \text{ ?} \]

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