Given that \(\displaystyle a,b,c,x,z,y \in \mathbb{R}\) and;

\[\begin{align} a^2&=by+cz\\ b^2&=cz+ax\\ c^2&=ax+by, \end{align}\]

find the value of \(\displaystyle \dfrac{x}{a+x} +\dfrac{y}{b+y} + \dfrac{z}{c+z} - 3.\)

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