Упростите выражение (x+y-4xy/(x+y))(y-x+4xy/(y-x)).

Ответ:

\[\left( x + y - \frac{4xy}{x + y} \right)\left( y - x + \frac{4xy}{y - x} \right) =\]

\[= \left( (x + y)^{\backslash x + y} - \frac{4xy}{x + y} \right) \cdot\]

\[\cdot \left( (y - x)^{\backslash y - x} + \frac{4xy}{y - x} \right) =\]

\[= \frac{x^{2} + 2xy + y^{2} - 4xy}{x + y} \cdot\]

\[\cdot \frac{y^{2} - 2yx + x^{2} + 4xy}{y - x} = \frac{x^{2} - 2xy + y^{2}}{x + y} \cdot\]

\[\cdot \frac{y^{2} + 2xy + x^{2}}{y - x} = \frac{(y - x)^{2}(y + x)^{2}}{(x + y)(y - x)} =\]

\[= (y - x)(y + x) = y^{2} - x^{2}\]