Question

помогите решить пример

Answer 1

$( frac{x-2y}{x^2 +2xy} - frac{x+2y}{x^2 -2xy} ) : frac{4y^2}{4y^2 -x^2} = \ \ =( frac{x-2y}{x(x+2y) } - frac{x+2y}{x(x-2y)} ) : frac{4y^2}{4y^2 -x^2} = \ \ = ( frac{(x-2y)(x-2y) - (x+2y)(x+2y)}{x(x+2y)(x-2y)} ) : frac{4y^2}{4y^2 -x^2} = \ \ =( frac{(x-2y)^2 - (x+2y)^2}{x(x+2y)(x-2y) } ) : frac{4y^2}{- 1 (x^2 - 4y^2)} = \ \ = frac{x^2 - 2*x*2y +(2y)^2 - (x^2 + 2*x*2y + (2y)^2 )}{x(x^2 - (2y)^2 )} * ( - frac{x^2-4y^2}{4y^2} ) =$
$= frac{x^2 - 2*x*2y +(2y)^2 - (x^2 + 2*x*2y + (2y)^2 )}{x(x^2 - (2y)^2 )} * ( - frac{x^2-4y^2}{4y^2} ) = \ \ = frac{x^2 - 4xy +4y^2 - x^2 -4xy -4y^2}{x(x^2 -4y^2)} * (- frac{x^2 -4y^2}{4y^2} )= \ \ = frac{-8xy}{x(x^2 -4y^2) } * (- frac{x^2 -4y^2}{4y^2} )= \ \ = - frac{8y }{x^2 -4y^2} * ( - frac{x^2 - 4y^2}{4y^2} ) = \ \ = frac{2*4y *(x^2 -4y^2)}{y*4y*(x^2 -4y^2)} = frac{2}{y}$