Solve 3/x-3=y

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

Solve for x

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

$$y\neq 0$$

Steps for Solving Linear Equation

Variable x cannot be equal to 3 since division by zero is not defined. Multiply both sides of the equation by x-3.

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

Use the distributive property to multiply y by x-3.

$$3=yx-3y$$

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

$$yx-3y=3$$

Add 3y to both sides.

$$yx=3+3y$$

The equation is in standard form.

$$yx=3y+3$$

Divide both sides by y.

$$\frac{yx}{y}=\frac{3y+3}{y}$$

Dividing by y undoes the multiplication by y.

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

Divide 3+3y by y.

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

Variable x cannot be equal to 3.

$$x=3+\frac{3}{y}\text{, }x\neq 3$$

Solve for y

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

$$x\neq 3$$

Steps for Solving Linear Equation

Multiply both sides of the equation by x-3.

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

Use the distributive property to multiply y by x-3.

$$3=yx-3y$$

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

$$yx-3y=3$$

Combine all terms containing y.

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

Divide both sides by x-3.

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

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

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