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$\dfrac{x}{1-x^2}+\dfrac{y}{1-y^2}+\dfrac{z}{1-z^2} \\ =\dfrac{kxyz}{(1-x^2)(1-y^2)(1-z^2)}$

If $x,y,$ and $z$ are real numbers satisfying $xy+yz+xz=1$, find the value of $k$ for which the equation above holds true.

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