Solve x+1/x=y

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

Solve for y

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

$$x\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by x.

$$xx+1=yx$$

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

$$x^{2}+1=yx$$

Swap sides so that all variable terms are on the left hand side.

$$yx=x^{2}+1$$

The equation is in standard form.

$$xy=x^{2}+1$$

Divide both sides by x.

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

Dividing by x undoes the multiplication by x.

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

Divide x^{2}+1 by x.

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

Solve for x (complex solution)

$$x=\frac{\sqrt{y^{2}-4}+y}{2}$$

$$x=\frac{-\sqrt{y^{2}-4}+y}{2}$$

Solve for x

$$x=\frac{\sqrt{y^{2}-4}+y}{2}$$

$$x=\frac{-\sqrt{y^{2}-4}+y}{2}\text{, }|y|\geq 2$$