Solve 1/r+1/s=1/d

$$\frac { 1 } { r } + \frac { 1 } { s } = \frac { 1 } { d }$$

Solve for d

$$d=\frac{rs}{r+s}$$

$$r\neq 0\text{ and }s\neq 0\text{ and }r\neq -s$$

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 drs, the least common multiple of r,s,d.

$$ds+dr=rs$$

Combine all terms containing d.

$$\left(s+r\right)d=rs$$

The equation is in standard form.

$$\left(r+s\right)d=rs$$

Divide both sides by r+s.

$$\frac{\left(r+s\right)d}{r+s}=\frac{rs}{r+s}$$

Dividing by r+s undoes the multiplication by r+s.

$$d=\frac{rs}{r+s}$$

Variable d cannot be equal to 0.

$$d=\frac{rs}{r+s}\text{, }d\neq 0$$

Solve for r

$$r=-\frac{ds}{d-s}$$

$$s\neq 0\text{ and }d\neq 0\text{ and }s\neq d$$

Steps for Solving Linear Equation

Variable r cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by drs, the least common multiple of r,s,d.

$$ds+dr=rs$$

Subtract rs from both sides.

$$ds+dr-rs=0$$

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

$$dr-rs=-ds$$

Combine all terms containing r.

$$\left(d-s\right)r=-ds$$

Divide both sides by d-s.

$$\frac{\left(d-s\right)r}{d-s}=-\frac{ds}{d-s}$$

Dividing by d-s undoes the multiplication by d-s.

$$r=-\frac{ds}{d-s}$$

Variable r cannot be equal to 0.

$$r=-\frac{ds}{d-s}\text{, }r\neq 0$$