query: How can I find the maximum value of $\frac{y}{xy+2y+1} + \frac{z}{yz+2z+1} + \frac{x}{xz+2x+1}$?
positive_passages.docid: 25203
positive_passages.text: with inequality $\frac{y}{xy+2y+1}+\frac{z}{yz+2z+1}+\frac{x}{zx+2x+1}\le\frac{3}{4}$
negative_passages.docid: 100900
negative_passages.text: Finding maxima and minima of $f(x,y)= x^4 + y^4 - 2x^2 - 2y^2 + 4xy$
negative_passages.docid: 8383
negative_passages.text: Are there any positive integers such that $\frac{x}{y} + \frac{y}{z} + \frac{z}{x} = 1$?
negative_passages.docid: 81437
negative_passages.text: Find the value of $y(1)$ of the ODE $y'+y=|x|$.
negative_passages.docid: 68990
negative_passages.text: Show that $\frac 1{1+x+y^{-1}}+\frac1{1+y+z^{-1}}+\frac1{1+z+x^{-1}}=1$ if $xyz=1$
negative_passages.docid: 13831
negative_passages.text: Find $ P(Z>X+Y)$ where $X,Y,Z \sim U(0,1)$ independently
negative_passages.docid: 82317
negative_passages.text: Find the minimum value of $A=\frac{2-a^3}{a}+\frac{2-b^3}{b}+\frac{2-c^3}{c}$
negative_passages.docid: 4278
negative_passages.text: Is $\frac{\vert x+y\vert}{1+\vert x+y\vert}\leq\frac{\vert x\vert}{1+\vert x\vert}+\frac{\vert y\vert}{1+\vert y\vert}$ true?
negative_passages.docid: 50283
negative_passages.text: Find answer of $\frac{x}{y+z}+\frac{y}{x+z}+\frac{z}{y+x}=4$
negative_passages.docid: 3885
negative_passages.text: Maximum and minimum of of $f(x)=|x-1|+|x-2|+|x-3|$
negative_passages.docid: 122186
negative_passages.text: Finding the maximum value of a function on an ellipse
negative_passages.docid: 158447
negative_passages.text: Limit as $(x,y)$ approaches $(0,0)$ of $(1+x^2+y^2)^{\frac{1}{x^2+y^2+xy^2}}$
negative_passages.docid: 17751
negative_passages.text: Find the greatest value of $\arg z$ achieved on a circle in $\mathbb{C}$
negative_passages.docid: 76441
negative_passages.text: Max. and Min. value of $|z|$ in $\left|z+\frac{2}{z}\right| = 2\,$
negative_passages.docid: 137522
negative_passages.text: Hard inequality $ (xy+yz+zx)\left(\frac{1}{(x+y)^2}+\frac{1}{(y+z)^2}+\frac{1}{(z+x)^2}\right)\ge\frac{9}{4} $
negative_passages.docid: 121362
negative_passages.text: If $A,B>0$ and $A+B = \frac{\pi}{3},$ Then find Maximum value of $\tan A\cdot \tan B$.
negative_passages.docid: 87513
negative_passages.text: Global maximum and minimum of $f(x,y,z)=xyz$ with the constraint $x^2+2y^2+3z^2=6$ with Lagrange multipliers?