$x,\,y,\,z \in \left [ 0,\,\frac{1}{3} \right )$, chứng minh rằng:
$$\frac{x^{2}}{x+ 1}+ \frac{y^{2}}{y+ 1}+ \frac{z^{2}}{z+ 1}\leqq \frac{3}{2}- \frac{\left ( \frac{1}{3}- x \right )}{2\left ( \frac{1}{3}- y \right )\left ( \frac{1}{3}- z \right )}$$
