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Algebra Level 3

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

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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