Solve z=xy/1+x=

$$z= \frac{ xy }{ 1+x } =$$

Solve for x

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

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 x+1.

$$z\left(x+1\right)=xy$$

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

$$zx+z=xy$$

Subtract xy from both sides.

$$zx+z-xy=0$$

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

$$zx-xy=-z$$

Combine all terms containing x.

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

Divide both sides by z-y.

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

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

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

Variable x cannot be equal to -1.

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

Solve for y

$$\left\{\begin{matrix}y=z+\frac{z}{x}\text{, }&x\neq 0\text{ and }x\neq -1\\y\in \mathrm{R}\text{, }&x=0\text{ and }z=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by x+1.

$$z\left(x+1\right)=xy$$

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

$$zx+z=xy$$

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

$$xy=zx+z$$

The equation is in standard form.

$$xy=xz+z$$

Divide both sides by x.

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

Dividing by x undoes the multiplication by x.

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

Divide zx+z by x.

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