Question

Упростите выражение:
$frac{1}{ x^{2} - 2xy} + frac{2}{4y^{2}- x^{2} } - frac{1}{ x^{2} + 2xy}$

Answer 1

$frac{1}{x^2-2xy}+frac{2}{4y^2-x^2}-frac{1}{x^2+2xy}=\\ frac{1}{x(x-2y)}-frac{2}{(x-2y)(x+2y)}-frac{1}{x(x+2y)}=frac{1*(x+2y)-2x-1*(x-2y)}{x(x-2y)(x+2y)}=\\ frac{x+2y-2x-x+2y}{x(x-2y)(x+2y)}=\\ frac{4y-2x}{x(x-2y)(x+2y)}=\\ frac{-2(x-2y)}{x(x-2y)(x+2y)}=\\ frac{-2}{x(x+2y)}$

Answer 2

1) 1/х(х-2у) - 2/(х-2у)(х+2у)=(х+2у)/х(х-2у)(х+2у) - 2х/(х-2у)(х+2у)=-1/х(х+2у)

2) -1/х(х+2у)- 1/х(х+2у)=-2/х(х+2у)

сделано по действии