Solve y=3-3x^2y/3

$$y = \frac { 3 - 3 x ^ { 2 } y } { 3 }$$

Solve for y (complex solution)

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

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

Steps for Solving Linear Equation

Subtract \frac{3-3x^{2}y}{3} from both sides.

$$y-\frac{3-3x^{2}y}{3}=0$$

Multiply both sides of the equation by 3.

$$3y-\left(3-3x^{2}y\right)=0$$

To find the opposite of 3-3x^{2}y, find the opposite of each term.

$$3y-3+3x^{2}y=0$$

Add 3 to both sides. Anything plus zero gives itself.

$$3y+3x^{2}y=3$$

Combine all terms containing y.

$$\left(3+3x^{2}\right)y=3$$

The equation is in standard form.

$$\left(3x^{2}+3\right)y=3$$

Divide both sides by 3+3x^{2}.

$$\frac{\left(3x^{2}+3\right)y}{3x^{2}+3}=\frac{3}{3x^{2}+3}$$

Dividing by 3+3x^{2} undoes the multiplication by 3+3x^{2}.

$$y=\frac{3}{3x^{2}+3}$$

Divide 3 by 3+3x^{2}.

$$y=\frac{1}{\left(x-i\right)\left(x+i\right)}$$

Solve for y

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

Steps for Solving Linear Equation

Subtract \frac{3-3x^{2}y}{3} from both sides.

$$y-\frac{3-3x^{2}y}{3}=0$$

Multiply both sides of the equation by 3.

$$3y-\left(3-3x^{2}y\right)=0$$

To find the opposite of 3-3x^{2}y, find the opposite of each term.

$$3y-3+3x^{2}y=0$$

Add 3 to both sides. Anything plus zero gives itself.

$$3y+3x^{2}y=3$$

Combine all terms containing y.

$$\left(3+3x^{2}\right)y=3$$

The equation is in standard form.

$$\left(3x^{2}+3\right)y=3$$

Divide both sides by 3+3x^{2}.

$$\frac{\left(3x^{2}+3\right)y}{3x^{2}+3}=\frac{3}{3x^{2}+3}$$

Dividing by 3+3x^{2} undoes the multiplication by 3+3x^{2}.

$$y=\frac{3}{3x^{2}+3}$$

Divide 3 by 3+3x^{2}.

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

Solve for x (complex solution)

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

$$x=\sqrt{-1+\frac{1}{y}}\text{, }y\neq 0$$

Solve for x

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

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