Solve 3/x=y-2/y

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

Solve for x

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

$$y\neq 0\text{ and }y\neq 2$$

Steps for Solving Linear Equation

Variable x 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.

$$y\times 3=x\left(y-2\right)$$

Use the distributive property to multiply x by y-2.

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

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

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

Combine all terms containing x.

$$\left(y-2\right)x=y\times 3$$

The equation is in standard form.

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

Divide both sides by y-2.

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

Dividing by y-2 undoes the multiplication by y-2.

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

Variable x cannot be equal to 0.

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

Solve for y

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

$$x\neq 0\text{ and }x\neq 3$$

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.

$$y\times 3=x\left(y-2\right)$$

Use the distributive property to multiply x by y-2.

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

Subtract xy from both sides.

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

Combine all terms containing y.

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

Divide both sides by 3-x.

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

Dividing by 3-x undoes the multiplication by 3-x.

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

Variable y cannot be equal to 0.

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