What is the value?

Algebra Level 2

Find the value of \(\frac{1}{1+\sqrt{2}}\)+\(\frac{1}{\sqrt{2}+\sqrt{3}}\)+\(\frac{1}{\sqrt{3}+\sqrt{4}}\)+\(\frac{1}{\sqrt{4}+\sqrt{5}}\)+\(\frac{1}{\sqrt{5}+\sqrt{6}}\)+\(\frac{1}{\sqrt{6}+\sqrt{7}}\)+\(\frac{1}{\sqrt{7}+\sqrt{8}}\)+\(\frac{1}{\sqrt{8}+\sqrt{9}}\)

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