Prove $\max\{x,y\}=\frac {(x-y)}{2} + \frac {(x+y)}{2}$
58629
Show that the $\max{ \{ x,y \} }= \frac{x+y+|x-y|}{2}$.
89170
How prove this inequality $\frac{x^2y}{z}+\frac{y^2z}{x}+\frac{z^2x}{y}\ge x^2+y^2+z^2$
25203
with inequality $\frac{y}{xy+2y+1}+\frac{z}{yz+2z+1}+\frac{x}{zx+2x+1}\le\frac{3}{4}$
39451
Proving inequation with maximum and 2nd derivative
32407
Prove $\exp(x+y) = \exp(x) \exp(y)$ for $\exp(x) = \sum_{n=0}^\infty \frac {x^n}{n!}$
90218
Proving $\frac{x}{y} +\frac{y}{z} + \frac{z}{x} \ge 3$ for positive $x,y,z$
143072
Proving $|\sin x - \sin y| < |x - y|$
1641
Proving $f' = - \frac{\partial{F}/\partial{x}}{\partial{F}/\partial{y}}$
124868
Prove that $\frac{bc}{b+c}+\frac{ca}{c+a}+\frac{ab}{a+b}<\frac{a+b+c}{2}$
146266
Find the maximum value of the expression ${\frac {x}{1+x^2}} + {\frac {y}{1+y^2}}+{\frac {z}{1+z^2}}$.
137614
$\left|\frac{x}{|x|}-\frac{y}{|y|}\right|\leq |x-y|$, for $|x|, |y|\geq 1$?
36837
Prove $\frac{1+a^{2}}{1+b+c^{2}} +\frac{1+b^{2}}{1+c+a^{2}} +\frac{1+c^{2}}{1+a+b^{2}} \geq 2$
145152
How to prove that $\frac{x^2}{yz+2}+\frac{y^2}{zx+2}+\frac{z^2}{xy+2}\geq \frac{x+y+z}{3}$ holds for any $(x,y,z)\in[1,2]^3$
82961
Show that $\left| \frac{1}{x}-\frac{1}{z} \right| \le \left|\frac{1}{x} - \frac{1}{y} \right| + \left|\frac{1}{y} - \frac{1}{z} \right|$.
76441
Max. and Min. value of $|z|$ in $\left|z+\frac{2}{z}\right| = 2\,$
54370
If $x+y+z=xyz$, prove $\frac{2x}{1-x^2}+\frac{2y}{1-y^2}+\frac{2z}{1-z^2}=\frac{2x}{1-x^2}\times\frac{2y}{1-y^2}\times\frac{2z}{1-z^2}$
94119
Prove that $xy \leq\frac{x^p}{p} + \frac{y^q}{q}$