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

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

Rešitev za c_T

$$c_{T}=\frac{36}{49}\approx 0,734693878$$

Koraki za reševanje linearnih enačb

Spremenljivka c_{T} ne more biti enaka vrednosti 0, ker deljenje z vrednostjo nič ni določeno. Pomnožite obe strani enačbe z 36c_{T}, najmanjšim skupnim mnogokratnikom števila c_{T},2,9,6,12.

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

Pomnožite 36 in \frac{1}{2}, da dobite \frac{36}{2}.

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

Delite 36 s/z 2, da dobite 18.

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

Pomnožite 36 in \frac{1}{9}, da dobite \frac{36}{9}.

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

Delite 36 s/z 9, da dobite 4.

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

Združite 18c_{T} in 4c_{T}, da dobite 22c_{T}.

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

Pomnožite 36 in \frac{1}{2}, da dobite \frac{36}{2}.

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

Delite 36 s/z 2, da dobite 18.

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

Združite 22c_{T} in 18c_{T}, da dobite 40c_{T}.

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

Pomnožite 36 in \frac{1}{6}, da dobite \frac{36}{6}.

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

Delite 36 s/z 6, da dobite 6.

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

Združite 40c_{T} in 6c_{T}, da dobite 46c_{T}.

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

Pomnožite 36 in \frac{1}{12}, da dobite \frac{36}{12}.

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

Delite 36 s/z 12, da dobite 3.

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

Združite 46c_{T} in 3c_{T}, da dobite 49c_{T}.

$$36=49c_{T}$$

Zamenjajte strani tako, da so vse spremenljivke na levi strani.

$$49c_{T}=36$$

Delite obe strani z vrednostjo 49.

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