Question

5/√7+√2 + 2/√5-√7 Вычислите

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Answer 1

$\frac{5}{\sqrt{7} +\sqrt{2} }+\frac{2}{\sqrt{5}-\sqrt{7}} =\frac{5*(\sqrt{7}-\sqrt{2})}{(\sqrt{7}+\sqrt{2})(\sqrt{7}-\sqrt{2})}+\frac{2*(\sqrt{5} +\sqrt{7}) }{(\sqrt{5}-\sqrt{7})(\sqrt{5}+\sqrt{7})}=\frac{5(\sqrt{7}-\sqrt{2})}{7-2}+\frac{2*(\sqrt{5}+\sqrt{7})}{5-7}=\frac{5*(\sqrt{7} -\sqrt{2}) }{5}-\frac{2*(\sqrt{5}+\sqrt{7})}{2}=\frac{10\sqrt{7}-10\sqrt{2}-10\sqrt{5} -10\sqrt{7}}{10}=-\frac{10\sqrt{2}+10\sqrt{5}}{10}=-(\sqrt{2}+\sqrt{5})$