Solve 1/c_{T}=1/2+1/9+1/2+frac{1}{6}+frac{1}{12}

$$\frac { 1 } { c _ { T } } = \frac { 1 } { 2 } + \frac { 1 } { 9 } + \frac { 1 } { 2 } + \frac { 1 } { 6 } + \frac { 1 } { 12 }$$

Solve for c_T

$$c_{T}=\frac{36}{49}\approx 0.734693878$$

Steps for Solving Linear Equation

Variable c_{T} cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 36c_{T}, the least common multiple of c_{T},2,9,6,12.

$$36=36c_{T}\times \frac{1}{2}+36c_{T}\times \frac{1}{9}+36c_{T}\times \frac{1}{2}+36c_{T}\times \frac{1}{6}+36c_{T}\times \frac{1}{12}$$

Multiply 36 and \frac{1}{2} to get \frac{36}{2}.

$$36=\frac{36}{2}c_{T}+36c_{T}\times \frac{1}{9}+36c_{T}\times \frac{1}{2}+36c_{T}\times \frac{1}{6}+36c_{T}\times \frac{1}{12}$$

Divide 36 by 2 to get 18.

$$36=18c_{T}+36c_{T}\times \frac{1}{9}+36c_{T}\times \frac{1}{2}+36c_{T}\times \frac{1}{6}+36c_{T}\times \frac{1}{12}$$

Multiply 36 and \frac{1}{9} to get \frac{36}{9}.

$$36=18c_{T}+\frac{36}{9}c_{T}+36c_{T}\times \frac{1}{2}+36c_{T}\times \frac{1}{6}+36c_{T}\times \frac{1}{12}$$

Divide 36 by 9 to get 4.

$$36=18c_{T}+4c_{T}+36c_{T}\times \frac{1}{2}+36c_{T}\times \frac{1}{6}+36c_{T}\times \frac{1}{12}$$

Combine 18c_{T} and 4c_{T} to get 22c_{T}.

$$36=22c_{T}+36c_{T}\times \frac{1}{2}+36c_{T}\times \frac{1}{6}+36c_{T}\times \frac{1}{12}$$

Multiply 36 and \frac{1}{2} to get \frac{36}{2}.

$$36=22c_{T}+\frac{36}{2}c_{T}+36c_{T}\times \frac{1}{6}+36c_{T}\times \frac{1}{12}$$

Divide 36 by 2 to get 18.

$$36=22c_{T}+18c_{T}+36c_{T}\times \frac{1}{6}+36c_{T}\times \frac{1}{12}$$

Combine 22c_{T} and 18c_{T} to get 40c_{T}.

$$36=40c_{T}+36c_{T}\times \frac{1}{6}+36c_{T}\times \frac{1}{12}$$

Multiply 36 and \frac{1}{6} to get \frac{36}{6}.

$$36=40c_{T}+\frac{36}{6}c_{T}+36c_{T}\times \frac{1}{12}$$

Divide 36 by 6 to get 6.

$$36=40c_{T}+6c_{T}+36c_{T}\times \frac{1}{12}$$

Combine 40c_{T} and 6c_{T} to get 46c_{T}.

$$36=46c_{T}+36c_{T}\times \frac{1}{12}$$

Multiply 36 and \frac{1}{12} to get \frac{36}{12}.

$$36=46c_{T}+\frac{36}{12}c_{T}$$

Divide 36 by 12 to get 3.

$$36=46c_{T}+3c_{T}$$

Combine 46c_{T} and 3c_{T} to get 49c_{T}.

$$36=49c_{T}$$

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

$$49c_{T}=36$$

Divide both sides by 49.

$$c_{T}=\frac{36}{49}$$