Solve 3xy+6x/3y=4

$$\frac { 3 x y + 6 x } { 3 y } = 4$$

Solve for x

$$x=\frac{4y}{y+2}$$

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

Steps for Solving Linear Equation

Multiply both sides of the equation by 3y.

$$3xy+6x=12y$$

Combine all terms containing x.

$$\left(3y+6\right)x=12y$$

Divide both sides by 3y+6.

$$\frac{\left(3y+6\right)x}{3y+6}=\frac{12y}{3y+6}$$

Dividing by 3y+6 undoes the multiplication by 3y+6.

$$x=\frac{12y}{3y+6}$$

Divide 12y by 3y+6.

$$x=\frac{4y}{y+2}$$

Solve for y

$$y=-\frac{2x}{x-4}$$

$$x\neq 0\text{ and }x\neq 4$$

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 3y.

$$3xy+6x=12y$$

Subtract 12y from both sides.

$$3xy+6x-12y=0$$

Subtract 6x from both sides. Anything subtracted from zero gives its negation.

$$3xy-12y=-6x$$

Combine all terms containing y.

$$\left(3x-12\right)y=-6x$$

Divide both sides by 3x-12.

$$\frac{\left(3x-12\right)y}{3x-12}=-\frac{6x}{3x-12}$$

Dividing by 3x-12 undoes the multiplication by 3x-12.

$$y=-\frac{6x}{3x-12}$$

Divide -6x by 3x-12.

$$y=-\frac{2x}{x-4}$$

Variable y cannot be equal to 0.

$$y=-\frac{2x}{x-4}\text{, }y\neq 0$$