Rational Function Equations

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!