Showing $d(x,y) = \frac{|x-y|}{1+|x-y|}$ is a distance.
141643
Showing $\rho (x,y)=\frac{d(x,y)}{1+d(x,y)}$ is a metric
23603
Joint distribution of $X+Y$ and $\frac{X}{X+Y}$
11289
Why $d(x) + d(y) \le n$ when proving Mantel's theorem
112329
Show that $d(z,a)=|\frac{z-a}{1-\overline{a}z}|$ is a metric on the unit disk
153794
What is the meaning of $1/(D+a)$, where $D$ is the derivative operator?
93427
Show that $\sum_{i=1}^{n} \frac {a_i}{1+a-a_i} + \prod_{i=1}^{n} {(1-a_i)} \leq 1$
85076
Is it true that $d(x,Y)=d(x,y_0)$ for some $y_0 \in Y$ when $Y$ is closed?
9355
If $d(x,y)$ is a metric, then $\frac{d(x,y)}{1 + d(x,y)}$ is also a metric
46106
Prove that $D_r \circ D_s = \{ (x,y) \in \mathbb{R}^2 \ | \ |x-y|<r+s \}$, where $D_a = \{ (x,y) \in \mathbb{R}^2\ | \ |x-y| < a \}$
82961
Show that $\left| \frac{1}{x}-\frac{1}{z} \right| \le \left|\frac{1}{x} - \frac{1}{y} \right| + \left|\frac{1}{y} - \frac{1}{z} \right|$.
121359
Show that $d_b(x,y)=\frac{d(x,y)}{1+d(x,y)}$ is a metric.
1641
Proving $f' = - \frac{\partial{F}/\partial{x}}{\partial{F}/\partial{y}}$
18530
Given 4 integers, $a, b, c, d > 0$, does $\frac{a}{b} < \frac{c}{d}$ imply $\frac{a}{b} < \frac{a+c}{b+d} < \frac{c}{d}$?
90218
Proving $\frac{x}{y} +\frac{y}{z} + \frac{z}{x} \ge 3$ for positive $x,y,z$
123674
Show that $y = \frac{2x}{x^2 +1}$ lies between $-1$ and $1$ inclusive.
117922
Is $\frac{a+b}{c+d}0$?
69082
Show that $\frac{X}{X+Y}\sim Beta(\alpha,\beta)$