Riješi 6a/a-5-3/6a-6

$$\frac { 6 a } { a - 5 } - \frac { 3 } { 6 a - 6 }$$

Izračunaj

$$\frac{12a^{2}-13a+5}{2\left(a-5\right)\left(a-1\right)}$$

Kratki koraci za rješenje

Rastavite 6a-6 na faktore.

$$\frac{6a}{a-5}-\frac{3}{6\left(a-1\right)}$$

Da biste zbrojili ili oduzeli izraze, proširite ih da bi imali iste nazivnike. Najmanji zajednički višekratnik brojeva a-5 i 6\left(a-1\right) jest 6\left(a-5\right)\left(a-1\right). Pomnožite \frac{6a}{a-5} i \frac{6\left(a-1\right)}{6\left(a-1\right)}. Pomnožite \frac{3}{6\left(a-1\right)} i \frac{a-5}{a-5}.

$$\frac{6a\times 6\left(a-1\right)}{6\left(a-5\right)\left(a-1\right)}-\frac{3\left(a-5\right)}{6\left(a-5\right)\left(a-1\right)}$$

Budući da \frac{6a\times 6\left(a-1\right)}{6\left(a-5\right)\left(a-1\right)} i \frac{3\left(a-5\right)}{6\left(a-5\right)\left(a-1\right)} imaju isti nazivnik, oduzmite ih oduzimanje njihovih brojnika.

$$\frac{6a\times 6\left(a-1\right)-3\left(a-5\right)}{6\left(a-5\right)\left(a-1\right)}$$

Pomnožite izraz 6a\times 6\left(a-1\right)-3\left(a-5\right).

$$\frac{36a^{2}-36a-3a+15}{6\left(a-5\right)\left(a-1\right)}$$

Kombinirajte slične izraze u 36a^{2}-36a-3a+15.

$$\frac{36a^{2}-39a+15}{6\left(a-5\right)\left(a-1\right)}$$

Rastavite na faktore izraze koji još nisu rastavljeni na faktore u izrazu \frac{36a^{2}-39a+15}{6\left(a-5\right)\left(a-1\right)}.

$$\frac{3\left(12a^{2}-13a+5\right)}{6\left(a-5\right)\left(a-1\right)}$$

Skratite 3 u brojniku i nazivniku.

$$\frac{12a^{2}-13a+5}{2\left(a-5\right)\left(a-1\right)}$$

Proširivanje broja 2\left(a-5\right)\left(a-1\right).

$$\frac{12a^{2}-13a+5}{2a^{2}-12a+10}$$

Faktor

$$\frac{12a^{2}-13a+5}{2\left(a-5\right)\left(a-1\right)}$$