Solve 3x+2/x=y

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

Solve for y

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

$$x\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by x.

$$3xx+2=yx$$

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

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

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

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

The equation is in standard form.

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

Divide both sides by x.

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

Dividing by x undoes the multiplication by x.

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

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

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

Solve for x (complex solution)

$$x=\frac{\sqrt{y^{2}-24}+y}{6}$$

$$x=\frac{-\sqrt{y^{2}-24}+y}{6}$$

Solve for x

$$x=\frac{\sqrt{y^{2}-24}+y}{6}$$

$$x=\frac{-\sqrt{y^{2}-24}+y}{6}\text{, }|y|\geq 2\sqrt{6}$$