Solve x(y+2)(y-2)=y-2

$$x(y+2)(y-2)=y-2$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=\frac{1}{y+2}\text{, }&y\neq -2\\x\in \mathrm{C}\text{, }&y=2\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply x by y+2.

$$\left(xy+2x\right)\left(y-2\right)=y-2$$

Use the distributive property to multiply xy+2x by y-2 and combine like terms.

$$xy^{2}-4x=y-2$$

Combine all terms containing x.

$$\left(y^{2}-4\right)x=y-2$$

Divide both sides by y^{2}-4.

$$\frac{\left(y^{2}-4\right)x}{y^{2}-4}=\frac{y-2}{y^{2}-4}$$

Dividing by y^{2}-4 undoes the multiplication by y^{2}-4.

$$x=\frac{y-2}{y^{2}-4}$$

Divide -2+y by y^{2}-4.

$$x=\frac{1}{y+2}$$

Solve for x

$$\left\{\begin{matrix}x=\frac{1}{y+2}\text{, }&y\neq -2\\x\in \mathrm{R}\text{, }&y=2\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply x by y+2.

$$\left(xy+2x\right)\left(y-2\right)=y-2$$

Use the distributive property to multiply xy+2x by y-2 and combine like terms.

$$xy^{2}-4x=y-2$$

Combine all terms containing x.

$$\left(y^{2}-4\right)x=y-2$$

Divide both sides by y^{2}-4.

$$\frac{\left(y^{2}-4\right)x}{y^{2}-4}=\frac{y-2}{y^{2}-4}$$

Dividing by y^{2}-4 undoes the multiplication by y^{2}-4.

$$x=\frac{y-2}{y^{2}-4}$$

Divide -2+y by y^{2}-4.

$$x=\frac{1}{y+2}$$

Solve for y

$$\left\{\begin{matrix}\\y=2\text{, }&\text{unconditionally}\\y=-2+\frac{1}{x}\text{, }&x\neq 0\end{matrix}\right.$$