Solve (x-3/y-3)(z-3)=z

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

Solve for x

$$x=-\frac{9-yz}{z-3}$$

$$y\neq 3\text{ and }z\neq 3$$

Steps for Solving Linear Equation

Multiply both sides of the equation by y-3.

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

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

$$xz-3x-3z+9=z\left(y-3\right)$$

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

$$xz-3x-3z+9=zy-3z$$

Add 3z to both sides.

$$xz-3x+9=zy-3z+3z$$

Combine -3z and 3z to get 0.

$$xz-3x+9=zy$$

Subtract 9 from both sides.

$$xz-3x=zy-9$$

Combine all terms containing x.

$$\left(z-3\right)x=zy-9$$

The equation is in standard form.

$$\left(z-3\right)x=yz-9$$

Divide both sides by z-3.

$$\frac{\left(z-3\right)x}{z-3}=\frac{yz-9}{z-3}$$

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

$$x=\frac{yz-9}{z-3}$$

Solve for y

$$\left\{\begin{matrix}y=\frac{xz-3x+9}{z}\text{, }&z\neq 3\text{ and }x\neq 3\text{ and }z\neq 0\\y\neq 3\text{, }&x=3\text{ and }z=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

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

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

$$xz-3x-3z+9=z\left(y-3\right)$$

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

$$xz-3x-3z+9=zy-3z$$

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

$$zy-3z=xz-3x-3z+9$$

Add 3z to both sides.

$$zy=xz-3x-3z+9+3z$$

Combine -3z and 3z to get 0.

$$zy=xz-3x+9$$

Divide both sides by z.

$$\frac{zy}{z}=\frac{xz-3x+9}{z}$$

Dividing by z undoes the multiplication by z.

$$y=\frac{xz-3x+9}{z}$$

Variable y cannot be equal to 3.

$$y=\frac{xz-3x+9}{z}\text{, }y\neq 3$$