Question

дпа, упростить выражение

Answer 1

$(frac{x-2y}{ x^{2} +2xy} - frac{x+2y}{ x^{2} -2xy} ): frac{4y^2}{4y^2-x^2} = \ \ (frac{x-2y}{ x(x+2y)} - frac{x+2y}{x(x-2y)} )* frac{4y^2-x^2}{4y^2} = \ \ frac{(x-2y)^2-(x+2y)^2}{x(x+2y)(x-2y)} * frac{4y^2-x^2}{4y^2} = \ \ frac{x^2-4xy+4y^2-x^2-4xy-4y^2}{x(x+2y)(x-2y)} * frac{4y^2-x^2}{4y^2} = \ \ frac{-8y}{x^2-4y^2} * frac{4y^2-x^2}{4y^2} = frac{2}{y}$