Solve x/y+xy-2=0

$$\frac { x } { y } + x y - 2 = 0$$

Solve for x (complex solution)

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

$$y\neq -i\text{ and }y\neq i\text{ and }y\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by y.

$$x+xyy+y\left(-2\right)=0$$

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

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

Subtract y\left(-2\right) from both sides. Anything subtracted from zero gives its negation.

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

Multiply -1 and -2 to get 2.

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

Combine all terms containing x.

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

The equation is in standard form.

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

Divide both sides by y^{2}+1.

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

Dividing by y^{2}+1 undoes the multiplication by y^{2}+1.

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

Solve for x

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

$$y\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by y.

$$x+xyy+y\left(-2\right)=0$$

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

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

Subtract y\left(-2\right) from both sides. Anything subtracted from zero gives its negation.

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

Multiply -1 and -2 to get 2.

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

Combine all terms containing x.

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

The equation is in standard form.

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

Divide both sides by 1+y^{2}.

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

Dividing by 1+y^{2} undoes the multiplication by 1+y^{2}.

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

Solve for y (complex solution)

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

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

Solve for y

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

$$y=\frac{-\sqrt{1-x^{2}}+1}{x}\text{, }x\neq 0\text{ and }|x|\leq 1$$