Answer
$y=-\frac{12}{x^{2}-2}$
Work Step by Step
2$x^{2}y-4y=-24$
Divide the equation by 2
a. $\frac{2x^{2}y}{2}=x^{2}y$
b. $\frac{-4y}{2}=-2y$
c.$\frac{-24}{2}=-12$
$x^{2}y-2y=-12$
The common term is y, so factor out y
$y(x^{2}-2)=-12$
To find y divide $y(x^{2}-2)$ by $(x^{2}-2)$
$\frac{y(x^{2}-2)}{x^{2}-2}$=
$y=-\frac{12}{x^{2}-2}$
