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

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

Resolver c_T

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

Pasos para resolver unha ecuación lineal

A variable c_{T} non pode ser igual a 0 porque a división entre cero non está definida. Multiplica ambos lados da ecuación por 36c_{T}, o mínimo común denominador de c_{T},2,9,6,12.

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

Multiplica 36 e \frac{1}{2} para obter \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 entre 2 para obter 18.

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

Multiplica 36 e \frac{1}{9} para obter \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 entre 9 para obter 4.

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

Combina 18c_{T} e 4c_{T} para obter 22c_{T}.

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

Multiplica 36 e \frac{1}{2} para obter \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 entre 2 para obter 18.

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

Combina 22c_{T} e 18c_{T} para obter 40c_{T}.

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

Multiplica 36 e \frac{1}{6} para obter \frac{36}{6}.

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

Divide 36 entre 6 para obter 6.

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

Combina 40c_{T} e 6c_{T} para obter 46c_{T}.

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

Multiplica 36 e \frac{1}{12} para obter \frac{36}{12}.

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

Divide 36 entre 12 para obter 3.

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

Combina 46c_{T} e 3c_{T} para obter 49c_{T}.

$$36=49c_{T}$$

Cambia de lado para que todos os termos variables estean no lado esquerdo.

$$49c_{T}=36$$

Divide ambos lados entre 49.

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