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If I have functions $f,g,h > 0$ and $f\le g+h$ then:

$$\frac f{f+1}\le \frac g{g+1}+\frac h{h+1}, x \in R$$

I have been trying to find out whether it's true or not but I haven't succeeded.

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    Assuming that you mean real-valued functions have you checked it for constant functions, (i.e. $f,g,h$ are real numbers)?2012-06-06
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    have you tried f=g+h, because x/(1+x) is increasing provided x>0.2012-06-06
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    The real number case Nils mentions is really the whole problem.2012-06-06

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