Упростить 2/(√5+√3) + 2/(√6+√4)+...+ 2/(√41+√39)

[latex] \frac{2}{\sqrt5+\sqrt3} + \frac{2}{\sqrt6+\sqrt4} + \frac{2}{\sqrt7+\sqrt5} +...+ \frac{2}{\sqrt{40}+\sqrt{39}} + \frac{2}{\sqrt{41}+\sqrt{39}} =\\\\= \frac{2(\sqrt5-\sqrt3)}{5-3} + \frac{2(\sqrt6-\sqrt4)}{6-4} + \frac{2(\sqrt7-\sqrt5)}{7-5} +...+ \frac{2(\sqrt{40}-\sqrt{48})}{40-38} + \frac{2(\sqrt{41}-\sqrt{39})}{41-39}=\\\\=\sqrt5-\sqrt3+\sqrt6-\sqrt4+\sqrt7-\sqrt5+\sqrt8-\sqrt6+\sqrt9-\sqrt7+[/latex] [latex]+\sqrt{10}-\sqrt8+...+\sqrt{38}-\sqrt{36}+\sqrt{39}-\sqrt{37}+\sqrt{40}-\sqrt{38}+[/latex]  [latex]+\sqrt{41}-\sqrt{39}=[/latex] [latex]\sqrt{41}+\sqrt{40}-\sqrt{4}-\sqrt3[/latex]