Упростите выражение: ((x+y)/(x-y)-(x-y)/(x+y)):(xy)/(x^2-y^2).

Ответ:

\[\left( \frac{x + y^{\backslash x + y}}{x - y} - \frac{x - y^{\backslash x - y}}{x + y} \right)\ :\frac{\text{xy}}{x^{2} - y^{2}} =\]

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

\[= \frac{4xy \cdot \left( x^{2} - y^{2} \right)}{\left( x^{2} - y^{2} \right) \cdot xy} = 4.\]