Equal in proportion

Algebra Level 4

2x2y+1z=120142y2z+1x=120142z2x+1y=12014 \begin{aligned} 2x-2y + \frac 1 z &=& \frac 1 {2014} \\ 2y - 2z + \frac 1 x &=& \frac 1 {2014} \\ 2z - 2x + \frac 1 y &=& \frac 1 {2014} \\ \end{aligned}

Find all positive real numbers x,y,zx,y,z such that they satisfy the system of equation above. Submit your answer as x+yzzxx + yz - zx .

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