Do the standard substitution $a=\frac{x}{y+z}, b= \frac{y}{z+x}, c= \frac{z}{x+y}$. I'm too lazy to LaTeX so much so I'll just write what I got after the substitution. LHS = $\frac{1}{x+y+z} \sum\frac{(y+z)(z+x)^2}{(y+z)^2 + (z+x)^2}$ $\leq \frac{1}{x+y+z} \sum\frac{(y+z)(z+x)^2}{2(y+z)(z+x)}$ All this question got is mugging up classic substitutions from 'Problems from the Book' unless I made some grave mistake in the simplification. If that is the case, how did it make it to the TST?

Just do this