Solve x+2=yxy

$$x+2=yxy$$

Solve for x (complex solution)

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

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

Steps for Solving Linear Equation

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

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

Subtract y^{2}x from both sides.

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

Subtract 2 from both sides. Anything subtracted from zero gives its negation.

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

Combine all terms containing x.

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

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

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

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

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

Solve for x

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

$$|y|\neq 1$$

Steps for Solving Linear Equation

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

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

Subtract y^{2}x from both sides.

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

Subtract 2 from both sides. Anything subtracted from zero gives its negation.

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

Combine all terms containing x.

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

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

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

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

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

Solve for y (complex solution)

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

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

Solve for y

$$y=\sqrt{\frac{x+2}{x}}$$

$$y=-\sqrt{\frac{x+2}{x}}\text{, }x\leq -2\text{ or }x>0$$