# What is the Maximum and minimum value of the given expression

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 $\mathbb{R}$

• what kind of numbers are $$x,y,z$$? – Dr. Sonnhard Graubner Jun 24 '17 at 15:40

The maximum does not exist. Try $x>-1$ and $xy+x+1\rightarrow0^+$.
The minimum does not exist. Try $x<-1$ and $xy+x+1\rightarrow0^+$.