Let \(a, b, c, x, y\) and \(z\) be real numbers such that \(a+x \neq 0, b+y \neq 0, c+z \neq 0,\) and
\(a^2=by+cz\)
\(b^2=cz+ax\)
\(c^2=ax+by\).
Find all possible values of \(\frac{x}{a + x} + \frac{y}{b + y} + \frac{z}{c + z}\).
I'm not sure where to start. Thanks in advance!