Find all rational solutions of $\frac{x}{x^2+4} + \frac{y}{y^2+4} = \frac{z}{z^2+4}$ or show non exist.
rational number solutions to $\frac{a}{a^2+1} + \frac{b}{b^2+1} = \frac{c}{c^2+1}$ with $abc\ne 0$