Question

Вычислите:
$frac{9}{5-sqrt{7} } + frac{22}{7+sqrt{5} } - frac{1}{sqrt{7}+sqrt{5} }$

Answer 1

См. фото

..................

Answer 2

$frac{9}{5-sqrt7}+frac{22}{7+sqrt5}-frac{1}{sqrt7+sqrt5}=\\=frac{9, (5+sqrt7)}{(5-sqrt7)(5+sqrt7)}+frac{22, (7-sqrt5)}{(7+sqrt5)(7-sqrt5)}-frac{sqrt7-sqrt5}{(sqrt7+sqrt5)(sqrt7-sqrt5)}=\\=frac{9(5+sqrt7)}{25-7}+frac{22(7-sqrt5)}{49-5}-frac{sqrt7-sqrt5}{7-5}=frac{5+sqrt7}{2}+frac{7-sqrt5}{2}-frac{sqrt7-sqrt5}{2}=\\=frac{5+sqrt7+7-sqrt5-sqrt7+sqrt5}{2}=frac{5+7}{2}=frac{12}{2}=6$