Question

упррастите выражение (фото)

Answer 1

1. 
$frac{2x}{x^2-4y^2}+frac{1}{x+2y}-frac{1}{2y-x}=frac{2x}{(x-2y)(x+2y)}+frac{1(x-2y)}{(x+2y)(x-2y)}-frac{1}{-(-2y+x)}=\\frac{2x+x-2y}{(x-2y)(x+2y)}+frac{1(x+2y)}{(x-2y)(x+2y)}=frac{3x-2y+x+2y}{(x-2y)(x+2y)}=frac{4x}{x^2-4y^2}$

2. 
$frac{x}{x^2-y^2}-frac{x}{(x-y)^2}*frac{(y-x)^2}{2x}-frac{x}{x+y}=\frac{x}{(x-y)(x+y)}-frac{x(x-y)}{(x+y)(x-y)}-frac{1}{(x-y)(x-y)}*frac{(y-x)(y-x)}{2}=\frac{x-x^2+xy}{(x-y)(x+y)}-frac{1}{-1(-x+y)(x-y)}*frac{(y-x)(y-x)}{2}=\frac{x-x^2+xy}{(x-y)(x+y)}-frac{1}{-1(x-y)}*frac{y-x}{2}=frac{x-x^2+xy}{(x-y)(x+y)}-frac{1}{-x+y}*frac{y-x}{2}=\frac{x-x^2+xy}{(x-y)(x+y)}-frac{1}{2}=frac{2(x-x^2+xy)}{2(x-y)(x+y)}-frac{1(x-y)(x+y)}{2(x-y)(x+y)}=frac{2x-2x^2+2xy-x^2+y^2}{2(x^2-y^2)}=$$frac{2x-3x^2+2xy+y^2}{2x^2-2y^2}$