Can anyone find the maximum and the minimum value of the following expression $$\frac{x+1}{xy+x+1}+\frac{y+1}{yz+y+1}+\frac{z+1}{zx+z+1}$$ for all $x,y,z$ belongs to $\mathbb{R}$
2026-04-08 04:10:41.1775621441
What is the Maximum and minimum value of the given expression
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The maximum does not exist. Try $x>-1$ and $xy+x+1\rightarrow0^+$.
The minimum does not exist. Try $x<-1$ and $xy+x+1\rightarrow0^+$.