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

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

Izračunaj c_T

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

Koraci rješavanja linearne jednadžbe

Varijabla c_{T} ne može biti jednaka 0 jer nije definirano dijeljenje nulom. Pomnožite obje strane jednadžbe s 36c_{T}, najmanjim zajedničkim višekratnikom brojeva 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 i \frac{1}{2} da biste dobili \frac{36}{2}.

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

Podijelite 36 s 2 da biste dobili 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 i \frac{1}{9} da biste dobili \frac{36}{9}.

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

Podijelite 36 s 9 da biste dobili 4.

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

Kombinirajte 18c_{T} i 4c_{T} da biste dobili 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 i \frac{1}{2} da biste dobili \frac{36}{2}.

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

Podijelite 36 s 2 da biste dobili 18.

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

Kombinirajte 22c_{T} i 18c_{T} da biste dobili 40c_{T}.

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

Pomnožite 36 i \frac{1}{6} da biste dobili \frac{36}{6}.

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

Podijelite 36 s 6 da biste dobili 6.

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

Kombinirajte 40c_{T} i 6c_{T} da biste dobili 46c_{T}.

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

Pomnožite 36 i \frac{1}{12} da biste dobili \frac{36}{12}.

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

Podijelite 36 s 12 da biste dobili 3.

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

Kombinirajte 46c_{T} i 3c_{T} da biste dobili 49c_{T}.

$$36=49c_{T}$$

Zamijenite strane tako da svi izrazi s nepoznanicama budu s lijeve strane.

$$49c_{T}=36$$

Podijelite obje strane sa 49.

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