Question

решите пример
$frac{ frac{1}{ sqrt{a - 1} } + sqrt{a + 1} }{ frac{1}{ sqrt{a + 1} } - frac{1}{ sqrt{a - 1} } } div frac{ sqrt{a + 1} }{(a - 1) sqrt{a + 1} - (a + 1) sqrt{a - 1} } =$

Answer 1

$mathtt{frac{frac{1}{sqrt{a-1}}+sqrt{a+1}}{frac{1}{sqrt{a+1}}-frac{1}{sqrt{a-1}}}:frac{sqrt{a+1}}{(sqrt{a-1})^2sqrt{a+1}-(sqrt{a+1})^2sqrt{a-1}}=}\\\mathtt{frac{1+sqrt{a-1}sqrt{a+1}}{sqrt{a-1}}*frac{sqrt{a+1}sqrt{a-1}}{sqrt{a-1}-sqrt{a+1}}*frac{sqrt{a-1}sqrt{a+1}(sqrt{a-1}-sqrt{a+1})}{sqrt{a+1}}=}\\mathtt{(1+sqrt{a-1}sqrt{a+1})(sqrt{a-1}sqrt{a+1})=sqrt{a^2-1}+a^2-1}$