$\frac{|x+y|}{|1+xy|}<1$ for $|x|<1$ and $|y|<1$
6100
Show that $\left|\frac{\alpha - \beta}{1-\bar{\alpha}\beta}\right| < 1$ when $|\alpha|,|\beta| < 1$
134535
Inequality $\frac{a}{b} + \frac{b}{c} + \frac{c}{a} \geq a + b+ c$ when $abc = 1$
27969
Why does $\frac{1}{x} < 4$ have two answers?
122115
Proving that $1+x^py^{1-p} \le (1+x)^p(1+y)^{1-p}$
69082
Show that $\frac{X}{X+Y}\sim Beta(\alpha,\beta)$
131847
$\frac{(x-1)(x+1)}{ (x+1)} \rightarrow (x-1)$ Domain Change
82612
Show that $\frac c {1+c} \le \frac a {1+a} + \frac b {1+b}$ , for $c \le a+b$ and $a,b,c \ge 0$
124868
Prove that $\frac{bc}{b+c}+\frac{ca}{c+a}+\frac{ab}{a+b}<\frac{a+b+c}{2}$
49209
Prove $(x+y)(y+z)(x+z)≤\frac8{27}(x+y+z)^3$
103851
Show that $\frac{xy}{z} + \frac{xz}{y} + \frac{yz}{x} \geq x+y+z $ by considering homogeneity
54513
Prove $\frac 1{x+1}<\ln\left(\frac{x+1}x\right)<0.5\left(\frac 1x+\frac 1{x+1}\right)$
28822
$|x| - |y| \leq |x-y|?$
45616
Find all solutions of ${\frac {1} {x} } + {\frac {1} {y} } +{\frac {1} {z}}=1$, where $x$, $y$ and $z$ are positive integers
33097
Proving an inequality without an integral: $\frac {1}{x+1}\leq \ln (1+x)- \ln (x) \leq \frac {1}{x}$
147785
Proving inequality $x^xy^y \geq (\frac{x+y}{2})^{x+y}$
121455
$f(x)$ if $f(xy)=f(x) +f(y) +\frac{x+y-1}{xy}$
8383
Are there any positive integers such that $\frac{x}{y} + \frac{y}{z} + \frac{z}{x} = 1$?