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$xy + x = \dfrac{3x + 2y + z + y + 2z}{3}\ |\cdot 3\\ 3xy + 3x = 3x + 2y + z + y + 2z\ | -3x\\ 3xy= 2y + z + y + 2z\ |\ \div (3y)\\ x=\dfrac{2}{3}+\dfrac{z}{3y}+\dfrac{1}{3}+\dfrac{2z}{3y}\ |\ add\ and\ reduce\\ \color{blue}x=\dfrac{z}{y}+1$

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