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Algebra Level 2

\[\large \color{red}{\frac{x^{2}}{y}} + \color{orange}{\frac{y^{2}}{z}} + \color{yellow}{\frac{z^{2}}{x}} - \color{green}{\frac{x^{3}}{2y^{2}}} - \color{blue}{\frac{y^{3}}{2z^{2}}} - \color{purple}{\frac{z^{3}}{2x^{2}}}\] Given that \(x,y,z\) are positive real numbers such that \(x+y+z=12\). Find the maximum value of the expression above.

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