Question

Prove that if \(x,y,z\)are positive real numbers then the following inequality holds
\( \frac {x+y}{x^2+y^2} + \frac {y+z}{y^2+z^2} + \frac {z+x}{z^2+x^2} \leq \frac 1x + \frac 1y + \frac 1z . \)