Question

Спростити вираз, СРОЧНО нужно​

Answer 1

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

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

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

$=\dfrac{x^2-4xy+4y^2-x^2-4xy-4y^2}{x(x^2-4y^2)}\cdot\dfrac{4y^2-x^2}{4y^2}=\dfrac{-8xy}{x(x^2-4y^2)}\cdot\dfrac{4y^2-x^2}{4y^2}=$

$=\dfrac{-8y}{x^2-4y^2}\cdot\dfrac{-x^2+4y^2}{4y^2}=-\dfrac{2}{x-4y^2}\cdot\dfrac{-(x-4y^2)}{y}=-\dfrac{2}{1}\bigg(-\dfrac1y\bigg)=\dfrac2y$