Solve 1/D=1/z+1/w

$$\frac { 1 } { D } = \frac { 1 } { z } + \frac { 1 } { w }$$

Solve for D

$$D=\frac{wz}{z+w}$$

$$w\neq 0\text{ and }z\neq 0\text{ and }z\neq -w$$

Steps for Solving Linear Equation

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

$$wz=Dw+Dz$$

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

$$Dw+Dz=wz$$

Combine all terms containing D.

$$\left(w+z\right)D=wz$$

The equation is in standard form.

$$\left(z+w\right)D=wz$$

Divide both sides by w+z.

$$\frac{\left(z+w\right)D}{z+w}=\frac{wz}{z+w}$$

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

$$D=\frac{wz}{z+w}$$

Variable D cannot be equal to 0.

$$D=\frac{wz}{z+w}\text{, }D\neq 0$$

Solve for w

$$w=-\frac{Dz}{D-z}$$

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

Steps for Solving Linear Equation

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

$$wz=Dw+Dz$$

Subtract Dw from both sides.

$$wz-Dw=Dz$$

Combine all terms containing w.

$$\left(z-D\right)w=Dz$$

Divide both sides by z-D.

$$\frac{\left(z-D\right)w}{z-D}=\frac{Dz}{z-D}$$

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

$$w=\frac{Dz}{z-D}$$

Variable w cannot be equal to 0.

$$w=\frac{Dz}{z-D}\text{, }w\neq 0$$