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**lllll** I'm having a great deal of difficulty trying to show that if $\displaystyle x, \ y, \ z \ \in \mathbb{R}^{+}$ and that $\displaystyle x \leq y+z$ then $\displaystyle \frac{x}{x+1} \leq \frac{y}{y+1} + \frac{z}{z+1}$

I've tryed working this thing out backwards, taking $\displaystyle \frac{x}{x+1} \leq \frac{y}{y+1} + \frac{z}{z+1}$ and trying to get $\displaystyle x \leq y+z$ but I got stuck in a loop or had a residue of 1.

I also tryed multiplying $\displaystyle x \leq y+z$ by their respective denominators, and their common denominator, but that let nowhere

$\displaystyle \color{red}\mbox{Well, it led me to the solution: I did this and got that }x < y+z+xyz+2yz$ $\displaystyle \color{red}\mbox{ and since we're given }x < y+z\,\mbox{ then we're done!}$

$\displaystyle \color{blue}Tonio$

Squaring didn't help either.

If anybody has any idea of how to approach this, it would be much appreciated.