Solve 1/z=1/x+1/y

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

Solve for x

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

$$y\neq 0\text{ and }z\neq 0\text{ and }z\neq y$$

Steps for Solving Linear Equation

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by xyz, the least common multiple of z,x,y.

$$xy=yz+xz$$

Subtract xz from both sides.

$$xy-xz=yz$$

Combine all terms containing x.

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

Divide both sides by y-z.

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

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

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

Variable x cannot be equal to 0.

$$x=\frac{yz}{y-z}\text{, }x\neq 0$$

Solve for y

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

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

Steps for Solving Linear Equation

Variable y cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by xyz, the least common multiple of z,x,y.

$$xy=yz+xz$$

Subtract yz from both sides.

$$xy-yz=xz$$

Combine all terms containing y.

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

Divide both sides by x-z.

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

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

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

Variable y cannot be equal to 0.

$$y=\frac{xz}{x-z}\text{, }y\neq 0$$