The motivation of this question is to look if there is such solution in rational number to the identity which mentioned here, I have done many attempts using Wolfram Alpha to find such pairs of rationals $(x,y,z)$ for which $\frac{x}{y+z}+\frac{y}{x+z}+\frac{z}{y+x}=1$ but I failed even I believed that there are 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