Simple rational functions

$\{x\colon x\neq 5\}()$ since $(x-5\neq 0)()$ , $(x\neq 5)()$

$\{x\colon x\neq 7\}()$ since $(x-7\neq 0)()$ , $(x\neq 7)()$

$\{x\colon x\neq \frac{5}{2}\}()$ since $5-2x\neq 0$ , $x\neq \frac{5}{2}$

$\{x\colon x\neq 3\lor -7\}$ since $x\neq 3$ and $x\neq -7$

$\{x\colon x\neq \frac{1}{2}\lor 3\}()$ since $2x^2-7x+3\neq 0$ , $(2x-1)(x-3)\neq 0$ , $2x-1\neq 0$ and $x-3\neq 0$ , $x\neq \frac{1}{2}$ and $x\neq 3$

$\{x\colon x\neq -5\}()$ since $(x+5)^2\neq 0$ , $x+5\neq 0$ , $x\neq -5$

$\{x\colon x\in \mathbb{R}\}()$ since $x^2+25\neq 0$ , $x^2\neq -25$ , $x\in \mathbb{R}$

$\{x\colon x\in \mathbb{R}\}()$ since $x^2+2\neq 0$ , $x^2\neq -2$ , $x\in \mathbb{R}$

$\{x\colon x\neq 3\}()$ since $\left|x-3\right|\neq 0$ , $x-3\neq 0$ , $x\neq 3$

$\{x\colon x\neq -4\lor 4\}$ since $\left|x\right|-4\neq 0$ , $\left|x\right|\neq 4$ , $x\neq -4$ and $x\neq 4$