Solve w/z-xy/1-x-y=0

$$\frac { w } { z } - \frac { x y } { 1 - x } - y = 0$$

Solve for w

$$w=\frac{yz}{1-x}$$

$$z\neq 0\text{ and }x\neq 1$$

Steps for Solving Linear Equation

Multiply both sides of the equation by z\left(x-1\right), the least common multiple of z,1-x.

$$\left(x-1\right)w-\left(-zxy\right)-yz\left(x-1\right)=0$$

Use the distributive property to multiply x-1 by w.

$$xw-w-\left(-zxy\right)-yz\left(x-1\right)=0$$

The opposite of -zxy is zxy.

$$xw-w+zxy-yz\left(x-1\right)=0$$

Use the distributive property to multiply -yz by x-1.

$$xw-w+zxy-yzx+yz=0$$

Combine zxy and -yzx to get 0.

$$xw-w+yz=0$$

Subtract yz from both sides. Anything subtracted from zero gives its negation.

$$xw-w=-yz$$

Reorder the terms.

$$wx-w=-yz$$

Combine all terms containing w.

$$\left(x-1\right)w=-yz$$

Divide both sides by x-1.

$$\frac{\left(x-1\right)w}{x-1}=-\frac{yz}{x-1}$$

Dividing by x-1 undoes the multiplication by x-1.

$$w=-\frac{yz}{x-1}$$

Solve for x

$$\left\{\begin{matrix}x=\frac{w-yz}{w}\text{, }&y\neq 0\text{ and }z\neq 0\text{ and }w\neq 0\\x\neq 1\text{, }&w=0\text{ and }y=0\text{ and }z\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Variable x cannot be equal to 1 since division by zero is not defined. Multiply both sides of the equation by z\left(x-1\right), the least common multiple of z,1-x.

$$\left(x-1\right)w-\left(-zxy\right)-yz\left(x-1\right)=0$$

Use the distributive property to multiply x-1 by w.

$$xw-w-\left(-zxy\right)-yz\left(x-1\right)=0$$

The opposite of -zxy is zxy.

$$xw-w+zxy-yz\left(x-1\right)=0$$

Use the distributive property to multiply -yz by x-1.

$$xw-w+zxy-yzx+yz=0$$

Combine zxy and -yzx to get 0.

$$xw-w+yz=0$$

Add w to both sides. Anything plus zero gives itself.

$$xw+yz=w$$

Subtract yz from both sides.

$$xw=w-yz$$

The equation is in standard form.

$$wx=w-yz$$

Divide both sides by w.

$$\frac{wx}{w}=\frac{w-yz}{w}$$

Dividing by w undoes the multiplication by w.

$$x=\frac{w-yz}{w}$$

Variable x cannot be equal to 1.

$$x=\frac{w-yz}{w}\text{, }x\neq 1$$