Prove $\frac{1}{x^2+yz}+\frac{1}{y^2+xz}+\frac{1}{z^2+xy} \le \frac{1}{2} (\frac{1}{xy}+\frac{1}{yz}+\frac{1}{xz})$ for $x,y,z \in \mathbb{R}_{+}^*$.
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