Complex Numbers Simplified?

Algebra Level 5

Let \(x,y,z\) be complex numbers such that the following equations hold. \[\begin{cases} x+y+z &= ~~~2 \\ x^2+y^2+z^2 &=~~~3 \\ xyz &=~~~4 \end{cases}\] Find the value of \[\dfrac{1}{xy+z-1}+\dfrac{1}{yz+x-1}+\dfrac{1}{zx+y-1}.\]

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