Solve 1/R=1/10+1/20+1/30

$$\frac { 1 } { R } = \frac { 1 } { 10 } + \frac { 1 } { 20 } + \frac { 1 } { 30 }$$

Solve for R

$$R = \frac{60}{11} = 5\frac{5}{11} \approx 5.454545455$$

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 60R, the least common multiple of R,10,20,30.

$$60=60R\times \frac{1}{10}+60R\times \frac{1}{20}+60R\times \frac{1}{30}$$

Multiply 60 and \frac{1}{10} to get \frac{60}{10}.

$$60=\frac{60}{10}R+60R\times \frac{1}{20}+60R\times \frac{1}{30}$$

Divide 60 by 10 to get 6.

$$60=6R+60R\times \frac{1}{20}+60R\times \frac{1}{30}$$

Multiply 60 and \frac{1}{20} to get \frac{60}{20}.

$$60=6R+\frac{60}{20}R+60R\times \frac{1}{30}$$

Divide 60 by 20 to get 3.

$$60=6R+3R+60R\times \frac{1}{30}$$

Combine 6R and 3R to get 9R.

$$60=9R+60R\times \frac{1}{30}$$

Multiply 60 and \frac{1}{30} to get \frac{60}{30}.

$$60=9R+\frac{60}{30}R$$

Divide 60 by 30 to get 2.

$$60=9R+2R$$

Combine 9R and 2R to get 11R.

$$60=11R$$

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

$$11R=60$$

Divide both sides by 11.

$$R=\frac{60}{11}$$