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$(\frac{a+b}{a-b}+\frac{a-b}{a+b}):(\frac{a^2}{a^2-b^2}+\frac{1}{\frac{a^2}{b^2}-1})=\frac{(a+b)^2+(a-b)^2}{(a+b)(a-b)}:(\frac{a^2}{a^2-b^2}+\frac{1}{\frac{a^2-b^2}{b^2}})=$

$\frac{a^2+2ab+b^2+a^2-2ab+b^2}{(a+b)(a-b)}:(\frac{a^2}{a^2-b^2}+\frac{b^2}{a^2-b^2}})=\frac{2a^2+2b^2}{a^2-b^2}*\frac{a^2-b^2}{a^2+b^2}=$

$=\frac{2(a^2+b^2)}{a^2+b^2}=2$

$(\frac{x^2y-xy^2}{x-y}+xy)(\frac{y}{x}+\frac{x}{y})=\frac{x^2y-xy^2+x^2y+xy^2}{x-y}*\frac{y^2+x^2}{xy}=\frac{2x^2y}{x-y}*\frac{y^2+x^2}{xy}$

$\frac{2x^2y}{x-y}*\frac{y^2+x^2}{xy}=\frac{2x(y^2+x^2)}{x-y}$

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