Exotic system of equations

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Solve the system:
$\frac{1}{x}+\frac{1}{y-z}=\frac{2}{3}$
$\frac{1}{y}+\frac{1}{z-x}=\frac{3}{4}$
$\frac{1}{z}+\frac{1}{x-y}=\frac{4}{5}$

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http://artofproblemsolving.com/communit ... 92p6240954 it is the solution of this system.