Solve x^2y-x^2-y=0

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

Solve for y (complex solution)

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

$$x\neq -1\text{ and }x\neq 1$$

Steps for Solving Linear Equation

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

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

Combine all terms containing y.

$$\left(x^{2}-1\right)y=x^{2}$$

Divide both sides by x^{2}-1.

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

Dividing by x^{2}-1 undoes the multiplication by x^{2}-1.

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

Solve for y

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

$$|x|\neq 1$$

Steps for Solving Linear Equation

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

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

Combine all terms containing y.

$$\left(x^{2}-1\right)y=x^{2}$$

Divide both sides by x^{2}-1.

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

Dividing by x^{2}-1 undoes the multiplication by x^{2}-1.

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

Solve for x (complex solution)

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

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

Solve for x

$$x=\sqrt{\frac{y}{y-1}}$$

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