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There is a function defined via a parameter $t\,(>0):$

$\cases{\begin{aligned} & y=t^2+\dfrac{1}{t} \\\\ & x=t-\dfrac{2}{t^2}. \end{aligned}}$

Find $\frac{dx}{dy}$ at $t=1.$

This problem is a part of <Christmas Streak 2017> series.

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