Question

5/√7+√2 + 2/√5-√7 Вычислите

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Answer 1

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