# An algebra problem by An Nguyen

Algebra Level pending

Let x, y, z be 3 positive real numbers such that $$x$$ + $$y$$ + $$z$$ = $$1$$. What's the maximum value of the following expression? $$\frac{x}{x + \sqrt{x + yz}}$$ + $$\frac{y}{y+ \sqrt{y + zx}}$$ + $$\frac{z}{z + \sqrt{z + xy}}$$

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