tex] Помогите, пожалуйста!...

July 2022 1 13 Report

[tex]( \frac{x - 2y}{ x^{2} + 2xy } - \frac{1}{ x^{2} - 4y^{2} } : \frac{x+2y}{(2y - x)^{2} }) * \frac{(x + 2y)^{2} }{ 4y^{2} }[/tex] Помогите, пожалуйста!

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Artem112

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$( \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 } 
$

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