$A=\frac{x+2}{2\left(x-2\right)}$
$x\neq 2\text{ and }x\neq 3$

$x=\frac{2\left(2A+1\right)}{2A-1}$
$A\neq \frac{1}{2}\text{ and }A\neq \frac{5}{2}$

$A=\frac{x+2}{2\left(x-2\right)}$
$x\neq 3\text{ and }x\neq 2$

$x=\frac{2\left(2A+1\right)}{2A-1}$
$A\neq \frac{5}{2}\text{ and }A\neq \frac{1}{2}$