Solve yx=z(1-x)

$$yx=z(1-x)$$

Solve for x

$$\left\{\begin{matrix}x=\frac{z}{y+z}\text{, }&y\neq -z\\x\in \mathrm{R}\text{, }&z=0\text{ and }y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$yx=z-zx$$

Add zx to both sides.

$$yx+zx=z$$

Combine all terms containing x.

$$\left(y+z\right)x=z$$

Divide both sides by y+z.

$$\frac{\left(y+z\right)x}{y+z}=\frac{z}{y+z}$$

Dividing by y+z undoes the multiplication by y+z.

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

Solve for y

$$\left\{\begin{matrix}y=-z+\frac{z}{x}\text{, }&x\neq 0\\y\in \mathrm{R}\text{, }&z=0\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$yx=z-zx$$

The equation is in standard form.

$$xy=z-xz$$

Divide both sides by x.

$$\frac{xy}{x}=\frac{z-xz}{x}$$

Dividing by x undoes the multiplication by x.

$$y=\frac{z-xz}{x}$$

Divide z-zx by x.

$$y=-z+\frac{z}{x}$$