Inegalitate simpluta, 1

[Claudiu Mindrila]

Fie \( x, \ y, \ z>0 \). Sa se arate ca: \( \frac{x\left(y+z\right)}{z+yz}+\frac{y\left(z+x\right)}{y+zx}+\frac{z\left(x+y\right)}{z+xy}\le2\left(\frac{x^{2}}{x+yz}+\frac{y^{2}}{y+zx}+\frac{z^{2}}{z+xy}\right) \)

Stefan Gavril

[Marius Mainea]

\( \sum\(\frac{xy}{x+yz}+\frac{yx}{y+zx}\)\le\sum\(\frac{x^2}{x+yz}+\frac{y^2}{y+zx}\) \)