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

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

Solve for y (complex solution)

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

Steps for Solving Linear Equation

Subtract 2x^{2} from both sides. Anything subtracted from zero gives its negation.

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

Add 2 to both sides.

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

Combine all terms containing y.

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

The equation is in standard form.

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

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

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

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

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

Divide -2x^{2}+2 by x^{2}-1.

$$y=-2$$

Solve for y

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

Steps for Solving Linear Equation

Subtract 2x^{2} from both sides. Anything subtracted from zero gives its negation.

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

Add 2 to both sides.

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

Combine all terms containing y.

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

The equation is in standard form.

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

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

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

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

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

Divide -2x^{2}+2 by x^{2}-1.

$$y=-2$$

Solve for x (complex solution)

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

Solve for x

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