Question

$( frac{x - 2y}{ x^{2} + 2xy } - frac{1}{ x^{2} - 4y^{2} } : frac{x+2y}{(2y - x)^{2} }) * frac{(x + 2y)^{2} }{ 4y^{2} }$ Помогите, пожалуйста!

Answer 1

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