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Algebra Level 4

\[\dfrac{\dfrac{\dfrac1{x^2} + \dfrac1{y^2}}{ \dfrac1{x^2} - \dfrac1{y^2} } - \dfrac{\dfrac1{x^2} - \dfrac1{y^2}}{ \dfrac1{x^2} + \dfrac1{y^2} } } {\left ( \dfrac8{\left( \dfrac{x+y}{x-y} + \dfrac{x-y}{x+y} \right) \left( \dfrac{x^2}{y^2} + \dfrac{y^2}{x^2} - 2 \right)}\right)} = \, ? \]

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