Solve 2/x-2/y=3x

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

Solve for y (complex solution)

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

$$x\neq 0\text{ and }x\neq -\frac{\sqrt{6}}{3}\text{ and }x\neq \frac{\sqrt{6}}{3}$$

Steps for Solving Linear Equation

Variable y cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by xy, the least common multiple of x,y.

$$y\times 2-x\times 2=3xxy$$

Multiply x and x to get x^{2}.

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

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

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

Multiply -1 and 2 to get -2.

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

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

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

Combine all terms containing y.

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

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

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

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

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

Variable y cannot be equal to 0.

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

Solve for y

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

$$x\neq 0\text{ and }|x|\neq \frac{\sqrt{6}}{3}$$

Steps for Solving Linear Equation

Variable y cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by xy, the least common multiple of x,y.

$$y\times 2-x\times 2=3xxy$$

Multiply x and x to get x^{2}.

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

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

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

Multiply -1 and 2 to get -2.

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

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

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

Combine all terms containing y.

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

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

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

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

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

Variable y cannot be equal to 0.

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

Solve for x

$$x=-\frac{\sqrt{6y^{2}+1}+1}{3y}$$

$$x=-\frac{-\sqrt{6y^{2}+1}+1}{3y}\text{, }y\neq 0$$