# Fungrim entry: 185efc

$\sqrt{\frac{z}{c - z}} = \sqrt{z} \sqrt{\frac{1}{c - z}}$
Assumptions:$z \in \mathbb{R} \;\mathbin{\operatorname{and}}\; c \in \left[0, \infty\right) \;\mathbin{\operatorname{and}}\; c - z \ne 0$
TeX:
\sqrt{\frac{z}{c - z}} = \sqrt{z} \sqrt{\frac{1}{c - z}}

z \in \mathbb{R} \;\mathbin{\operatorname{and}}\; c \in \left[0, \infty\right) \;\mathbin{\operatorname{and}}\; c - z \ne 0
Definitions:
Fungrim symbol Notation Short description
Sqrt$\sqrt{z}$ Principal square root
RR$\mathbb{R}$ Real numbers
ClosedOpenInterval$\left[a, b\right)$ Closed-open interval
Infinity$\infty$ Positive infinity
Source code for this entry:
Entry(ID("185efc"),
Formula(Equal(Sqrt(Div(z, Sub(c, z))), Mul(Sqrt(z), Sqrt(Div(1, Sub(c, z)))))),
Variables(z, c),
Assumptions(And(Element(z, RR), Element(c, ClosedOpenInterval(0, Infinity)), NotEqual(Sub(c, z), 0))))

## Topics using this entry

Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2021-03-15 19:12:00.328586 UTC