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 $\mathbb{R}$

  • 1
    $\begingroup$ what kind of numbers are $$x,y,z$$? $\endgroup$ – 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 $xy+x+1\rightarrow0^+$.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.