Question

Упростите
$( \frac{a^2}{a+n} - \frac{a^2}{a^4+n^2+2an})/ (\frac{a^2}{a-n}- \frac{a^2}{a^2-n^2})$

Answer 1

$(\frac{a^2}{a+n}- \frac{a^2}{(a+n)^2})/( \frac{a^2}{a-n}-\frac{a^2}{(a-n)(a+n)})= \\ = \frac{a^2(a+n)-a^2}{(a+n)^2}/ \frac{a^2(a+n)-a^2}{(a-n)(a+n)}= \frac{a^2(a+n)-a^2}{(a+n)^2}* \frac{(a-n)(a+n)}{a^2(a+n)-a^2}= \frac{a-n}{a+n}$