Solve 6(x-y)=xy

$$6 ( x - y ) = x y$$

Solve for x

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

$$y\neq 6$$

Steps for Solving Linear Equation

Use the distributive property to multiply 6 by x-y.

$$6x-6y=xy$$

Subtract xy from both sides.

$$6x-6y-xy=0$$

Add 6y to both sides. Anything plus zero gives itself.

$$6x-xy=6y$$

Combine all terms containing x.

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

Divide both sides by -y+6.

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

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

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

Solve for y

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

$$x\neq -6$$

Steps for Solving Linear Equation

Use the distributive property to multiply 6 by x-y.

$$6x-6y=xy$$

Subtract xy from both sides.

$$6x-6y-xy=0$$

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

$$-6y-xy=-6x$$

Combine all terms containing y.

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

The equation is in standard form.

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

Divide both sides by -6-x.

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

Dividing by -6-x undoes the multiplication by -6-x.

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

Divide -6x by -6-x.

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