The motivation of this question is to look if there is such solution in rational number to the identity which montioned here, I have done many attempts using wolfram alpha to find such pairs of rational $(x,y,z)$ for which $\frac{x}{y+z}+\frac{y}{x+z}+\frac{z}{y+x}=1$ in rational but I failed even I believed that there is no such solutions ?
How I can prove or disprove that $\frac{x}{y+z}+\frac{y}{x+z}+\frac{z}{y+x}=1$ has solutions in rationals?
user157361