# System of Complex Equations

Algebra Level 3

$$x, y$$ and $$z$$ are complex numbers that satisfy the equations $$x+y+z = 2$$, $$xy + yz + zx = 3$$ and $$xyz =4$$. Given that $$\frac {1}{1-x-yz} + \frac {1}{1-y-zx} + \frac {1}{1-z-xy} = \frac {a}{b}$$, where $$a$$ and $$b$$ are coprime positive integers, what is the value of $$a+b$$?

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