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

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