Найдите значение выражения (1/x+1/y):(1/x-1/y) при x=-2; y=4.

\[\left( \frac{1^{\backslash y}}{x} + \frac{1^{\backslash x}}{y} \right)\ :\left( \frac{1^{\backslash y}}{x} - \frac{1^{\backslash x}}{y} \right) =\]

\[= \frac{y + x}{\text{xy}}\ :\frac{y - x}{\text{xy}} =\]

\[= \frac{y + x}{\text{xy}} \cdot \frac{\text{xy}}{y - x} = \frac{y + x}{y - x};\]

\[x = - 2;\ \ y = 4:\]

\[\frac{4 - 2}{4 + 2} = \frac{2}{6} = \frac{1}{3}.\]