Find \( \frac{d y}{d x} \), if \( x \) and \( y \) are connected pa...

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Find \( \frac{d y}{d x} \), if \( x \) and \( y \) are connected parametrically by the equations, given below without eliminating the parameter.
\[
x=a \sqrt{\frac{t^{2}-1}{t^{2}+1}}, y=a t \sqrt{\frac{t^{2}-1}{t^{2}+1}}
\]
\( \mathrm{P} \)
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