Question

Спростiть вираз. Умоляю, пожалуйста. СРОЧНО

Answer 1

$\dfrac{y^2-x^2}{4xy-(x+y)^2}-\dfrac{x-y}{x+y}=\dfrac{(y-x)(y+x)}{4xy-(x^2+2xy+y^2)}-\dfrac{x-y}{x+y}=$

$=\dfrac{(y-x)(y+x)}{-x^2+2xy-y^2}-\dfrac{x-y}{x+y}=\dfrac{-(x-y)(y+x)}{-(x-y)^2}-\dfrac{x-y}{x+y}=$

$=\dfrac{y+x}{x-y}-\dfrac{x-y}{x+y}=\dfrac{(y+x)(x+y)-(x-y)(x-y)}{(x-y)(x+y)}=$

$=\dfrac{x^2+2xy+y^2-(x^2-2xy+y^2)}{(x-y)(x+y)}=\dfrac{x^2+2xy+y^2-x^2+2xy-y^2}{(x-y)(x+y)}=$

$=\dfrac{4xy}{x^2-y^2}$