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If $x=\frac{4\sqrt{2}}{\sqrt{2}+1}$

Then the value of

$\frac{1}{\sqrt{2}}(\frac{x+2}{x-2}+\frac{x+2\sqrt{2}}{x-2\sqrt{2}})$

can be simplified to a number of the form $\sqrt{k}$ where $k$ is a positive integer.Find $k$

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