Solve W/2-xy/1-x-y=0

$$\frac { W } { 2 } - \frac { x y } { 1 - x } - y = 0$$

Solve for W

$$W=\frac{2y}{1-x}$$

$$x\neq 1$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2\left(x-1\right), the least common multiple of 2,1-x.

$$\left(x-1\right)W+2xy-y\times 2\left(x-1\right)=0$$

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

$$xW-W+2xy-y\times 2\left(x-1\right)=0$$

Multiply -1 and 2 to get -2.

$$xW-W+2xy-2y\left(x-1\right)=0$$

Use the distributive property to multiply -2y by x-1.

$$xW-W+2xy-2yx+2y=0$$

Combine 2xy and -2yx to get 0.

$$xW-W+2y=0$$

Subtract 2y from both sides. Anything subtracted from zero gives its negation.

$$xW-W=-2y$$

Combine all terms containing W.

$$\left(x-1\right)W=-2y$$

Divide both sides by x-1.

$$\frac{\left(x-1\right)W}{x-1}=-\frac{2y}{x-1}$$

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

$$W=-\frac{2y}{x-1}$$

Solve for x

$$\left\{\begin{matrix}x=\frac{W-2y}{W}\text{, }&y\neq 0\text{ and }W\neq 0\\x\neq 1\text{, }&W=0\text{ and }y=0\end{matrix}\right.$$

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 2\left(x-1\right), the least common multiple of 2,1-x.

$$\left(x-1\right)W+2xy-y\times 2\left(x-1\right)=0$$

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

$$xW-W+2xy-y\times 2\left(x-1\right)=0$$

Multiply -1 and 2 to get -2.

$$xW-W+2xy-2y\left(x-1\right)=0$$

Use the distributive property to multiply -2y by x-1.

$$xW-W+2xy-2yx+2y=0$$

Combine 2xy and -2yx to get 0.

$$xW-W+2y=0$$

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

$$xW+2y=W$$

Subtract 2y from both sides.

$$xW=W-2y$$

The equation is in standard form.

$$Wx=W-2y$$

Divide both sides by W.

$$\frac{Wx}{W}=\frac{W-2y}{W}$$

Dividing by W undoes the multiplication by W.

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

Variable x cannot be equal to 1.

$$x=\frac{W-2y}{W}\text{, }x\neq 1$$