Solve 1/RT=1/15+1/60+11/20+frac{1}{30}=

$$\frac { 1 } { R T } = \frac { 1 } { 15 } + \frac { 1 } { 60 } + \frac { 11 } { 20 } + \frac { 1 } { 30 } =$$

Solve for R

$$R=\frac{3}{2T}$$

$$T\neq 0$$

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 60RT, the least common multiple of RT,15,60,20,30.

$$60=60RT\times \frac{1}{15}+60RT\times \frac{1}{60}+60RT\times \frac{11}{20}+60RT\times \frac{1}{30}$$

Multiply 60 and \frac{1}{15} to get 4.

$$60=4RT+60RT\times \frac{1}{60}+60RT\times \frac{11}{20}+60RT\times \frac{1}{30}$$

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

$$60=4RT+RT+60RT\times \frac{11}{20}+60RT\times \frac{1}{30}$$

Combine 4RT and RT to get 5RT.

$$60=5RT+60RT\times \frac{11}{20}+60RT\times \frac{1}{30}$$

Multiply 60 and \frac{11}{20} to get 33.

$$60=5RT+33RT+60RT\times \frac{1}{30}$$

Combine 5RT and 33RT to get 38RT.

$$60=38RT+60RT\times \frac{1}{30}$$

Multiply 60 and \frac{1}{30} to get 2.

$$60=38RT+2RT$$

Combine 38RT and 2RT to get 40RT.

$$60=40RT$$

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

$$40RT=60$$

The equation is in standard form.

$$40TR=60$$

Divide both sides by 40T.

$$\frac{40TR}{40T}=\frac{60}{40T}$$

Dividing by 40T undoes the multiplication by 40T.

$$R=\frac{60}{40T}$$

Divide 60 by 40T.

$$R=\frac{3}{2T}$$

Variable R cannot be equal to 0.

$$R=\frac{3}{2T}\text{, }R\neq 0$$

Solve for T

$$T=\frac{3}{2R}$$

$$R\neq 0$$

Steps for Solving Linear Equation

Variable T cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 60RT, the least common multiple of RT,15,60,20,30.

$$60=60RT\times \frac{1}{15}+60RT\times \frac{1}{60}+60RT\times \frac{11}{20}+60RT\times \frac{1}{30}$$

Multiply 60 and \frac{1}{15} to get 4.

$$60=4RT+60RT\times \frac{1}{60}+60RT\times \frac{11}{20}+60RT\times \frac{1}{30}$$

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

$$60=4RT+RT+60RT\times \frac{11}{20}+60RT\times \frac{1}{30}$$

Combine 4RT and RT to get 5RT.

$$60=5RT+60RT\times \frac{11}{20}+60RT\times \frac{1}{30}$$

Multiply 60 and \frac{11}{20} to get 33.

$$60=5RT+33RT+60RT\times \frac{1}{30}$$

Combine 5RT and 33RT to get 38RT.

$$60=38RT+60RT\times \frac{1}{30}$$

Multiply 60 and \frac{1}{30} to get 2.

$$60=38RT+2RT$$

Combine 38RT and 2RT to get 40RT.

$$60=40RT$$

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

$$40RT=60$$

Divide both sides by 40R.

$$\frac{40RT}{40R}=\frac{60}{40R}$$

Dividing by 40R undoes the multiplication by 40R.

$$T=\frac{60}{40R}$$

Divide 60 by 40R.

$$T=\frac{3}{2R}$$

Variable T cannot be equal to 0.

$$T=\frac{3}{2R}\text{, }T\neq 0$$