Question

Упростите выражение по алгебре

Answer 1

$( \frac{2a}{a+1}+ \frac{2}{a-1}+ \frac{4a}{a^2-1})( \frac{2a}{a+1}+ \frac{2}{a-1}- \frac{4a}{a^2-1})=\\ ( \frac{2a(a-1)+2(a+1)}{a^2-1}+ \frac{4a}{a^2-1})( \frac{2a(a-1)+2(a+1)}{a^2-1}- \frac{4a}{a^2-1})=\\ ( \frac{2a^2-2a+2a+2}{a^2-1}+ \frac{4a}{a^2-1})( \frac{2a^2-2a+2a+2}{a^2-1}- \frac{4a}{a^2-1})=\\ ( \frac{2a^2+2+4a}{a^2-1})( \frac{2a^2+2-4a}{a^2-1})= ( \frac{2(a^2+2a+1)}{a^2-1})( \frac{2(a^2-2a+1)}{a^2-1})=$
$4( \frac{(a+1)^2}{a^2-1})( \frac{(a-1)^2}{a^2-1})=4( \frac{a+1}{a-1})( \frac{a-1}{a+1})=4$