Solve x^2y-x^2-4xy+4y=0

$$x ^ { 2 } y - x ^ { 2 } - 4 x y + 4 y = 0$$

Solve for y

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

$$x\neq 2$$

Steps for Solving Linear Equation

Add x^{2} to both sides. Anything plus zero gives itself.

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

Combine all terms containing y.

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

Divide both sides by x^{2}-4x+4.

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

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

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

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

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

Solve for x (complex solution)

$$\left\{\begin{matrix}x=\frac{2\sqrt{y}\left(\sqrt{y}+1\right)}{y-1}\text{; }x=\frac{2\sqrt{y}\left(\sqrt{y}-1\right)}{y-1}\text{, }&y\neq 1\\x=1\text{, }&y=1\end{matrix}\right.$$

Solve for x

$$\left\{\begin{matrix}x=\frac{2\sqrt{y}\left(\sqrt{y}+1\right)}{y-1}\text{; }x=\frac{2\sqrt{y}\left(\sqrt{y}-1\right)}{y-1}\text{, }&y\neq 1\text{ and }y\geq 0\\x=1\text{, }&y=1\end{matrix}\right.$$