$x=-\left(y-1\right)^{-\frac{1}{2}}\sqrt{y}$
$x=\left(y-1\right)^{-\frac{1}{2}}\sqrt{y}\text{, }y\neq 1$

$y=\frac{x^{2}}{x^{2}-1}$
$x\neq -1\text{ and }x\neq 1$

$x=\sqrt{\frac{y}{y-1}}$
$x=-\sqrt{\frac{y}{y-1}}\text{, }y>1\text{ or }y\leq 0$

$y=\frac{x^{2}}{x^{2}-1}$
$|x|\neq 1$