$$H=\frac{(x+2)(2+x-3)}{(x^{2}-1)(x+2)}$$
$H=\frac{1}{x+1}$
$x\neq -1\text{ and }x\neq 1\text{ and }x\neq -2$
$x=-1+\frac{1}{H}$
$H\neq 0\text{ and }H\neq \frac{1}{2}\text{ and }H\neq -1$
$H=\frac{1}{x+1}$
$x\neq -2\text{ and }|x|\neq 1$
$x=-1+\frac{1}{H}$
$H\neq \frac{1}{2}\text{ and }H\neq 0\text{ and }H\neq -1$
