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Algebra Level 3

x1x2+y1y2+z1z2=kxyz(1x2)(1y2)(1z2)\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,x,y, and zz are real numbers satisfying xy+yz+xz=1xy+yz+xz=1, find the value of kk for which the equation above holds true.

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