# So complicated

Algebra Level 3

Given $$x$$ and $$y$$ are distinct real numbers such that $\frac{x^{2}+y^{2}}{x^{2}-y^{2}}+\frac{x^{2}-y^{2}}{x^{2}+y^{2}}=4$ If $\frac{x^{8}+y^{8}}{x^{8}-y^{8}}+\frac{x^{8}-y^{8}}{x^{8}+y^{8}}$ can be expressed as $$\frac{a}{b}$$, where $$a$$ and $$b$$ are positive numbers and $$\text{gcd}(a,b)=1$$, find $$a+b$$.

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