Упростите выражение: ((x+y)/y-(x+y)/x):(3(y+x))/xy.

\[\left( \frac{x + y^{\backslash x}}{y} - \frac{x + y^{\backslash y}}{x} \right)\ :\frac{3(y + x)}{\text{xy}} =\]

\[= \frac{x^{2} + xy - xy - y^{2}}{\text{xy}} \cdot \frac{\text{xy}}{3(y + x)} =\]

\[= \frac{x^{2} - y^{2}}{\text{xy}} \cdot \frac{\text{xy}}{3(x + y)} =\]

\[= \frac{(x - y)(x + y)}{3(x + y)} = \frac{x - y}{3}.\]