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

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

Solve for x

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

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

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 x,y,z.

$$yz+xz=xy$$

Subtract xy from both sides.

$$yz+xz-xy=0$$

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

$$xz-xy=-yz$$

Reorder the terms.

$$-xy+xz=-yz$$

Combine all terms containing x.

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

The equation is in standard form.

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

Divide both sides by -y+z.

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

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

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

Variable x cannot be equal to 0.

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

Solve for y

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

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

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 x,y,z.

$$yz+xz=xy$$

Subtract xy from both sides.

$$yz+xz-xy=0$$

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

$$yz-xy=-xz$$

Reorder the terms.

$$-xy+yz=-xz$$

Combine all terms containing y.

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

The equation is in standard form.

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

Divide both sides by z-x.

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

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

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

Variable y cannot be equal to 0.

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