Riješi 24/x-3+15/3x+1

$$\frac{24}{x-3} + \frac{15}{3x+1}$$

Izračunaj

$$\frac{3\left(29x-7\right)}{\left(x-3\right)\left(3x+1\right)}$$

Kratki koraci za rješenje

Da biste zbrojili ili oduzeli izraze, proširite ih da bi imali iste nazivnike. Najmanji zajednički višekratnik brojeva x-3 i 3x+1 jest \left(x-3\right)\left(3x+1\right). Pomnožite \frac{24}{x-3} i \frac{3x+1}{3x+1}. Pomnožite \frac{15}{3x+1} i \frac{x-3}{x-3}.

$$\frac{24\left(3x+1\right)}{\left(x-3\right)\left(3x+1\right)}+\frac{15\left(x-3\right)}{\left(x-3\right)\left(3x+1\right)}$$

Budući da \frac{24\left(3x+1\right)}{\left(x-3\right)\left(3x+1\right)} i \frac{15\left(x-3\right)}{\left(x-3\right)\left(3x+1\right)} imaju isti nazivnik, zbrojite ih zbrajanjem njihovih brojnika.

$$\frac{24\left(3x+1\right)+15\left(x-3\right)}{\left(x-3\right)\left(3x+1\right)}$$

Pomnožite izraz 24\left(3x+1\right)+15\left(x-3\right).

$$\frac{72x+24+15x-45}{\left(x-3\right)\left(3x+1\right)}$$

Kombinirajte slične izraze u 72x+24+15x-45.

$$\frac{87x-21}{\left(x-3\right)\left(3x+1\right)}$$

Proširivanje broja \left(x-3\right)\left(3x+1\right).

$$\frac{87x-21}{3x^{2}-8x-3}$$

Faktor

$$\frac{3\left(29x-7\right)}{\left(x-3\right)\left(3x+1\right)}$$