Riješi 4w/w^2+9w+14-2w+5/w^2+3w-28

$$\frac { 4 w } { w ^ { 2 } + 9 w + 14 } - \frac { 2 w + 5 } { w ^ { 2 } + 3 w - 28 }$$

Izračunaj

$$\frac{2w^{2}-25w-10}{\left(w-4\right)\left(w+2\right)\left(w+7\right)}$$

Kratki koraci za rješenje

Rastavite w^{2}+9w+14 na faktore. Rastavite w^{2}+3w-28 na faktore.

$$\frac{4w}{\left(w+2\right)\left(w+7\right)}-\frac{2w+5}{\left(w-4\right)\left(w+7\right)}$$

Da biste zbrojili ili oduzeli izraze, proširite ih da bi imali iste nazivnike. Najmanji zajednički višekratnik brojeva \left(w+2\right)\left(w+7\right) i \left(w-4\right)\left(w+7\right) jest \left(w-4\right)\left(w+2\right)\left(w+7\right). Pomnožite \frac{4w}{\left(w+2\right)\left(w+7\right)} i \frac{w-4}{w-4}. Pomnožite \frac{2w+5}{\left(w-4\right)\left(w+7\right)} i \frac{w+2}{w+2}.

$$\frac{4w\left(w-4\right)}{\left(w-4\right)\left(w+2\right)\left(w+7\right)}-\frac{\left(2w+5\right)\left(w+2\right)}{\left(w-4\right)\left(w+2\right)\left(w+7\right)}$$

Budući da \frac{4w\left(w-4\right)}{\left(w-4\right)\left(w+2\right)\left(w+7\right)} i \frac{\left(2w+5\right)\left(w+2\right)}{\left(w-4\right)\left(w+2\right)\left(w+7\right)} imaju isti nazivnik, oduzmite ih oduzimanje njihovih brojnika.

$$\frac{4w\left(w-4\right)-\left(2w+5\right)\left(w+2\right)}{\left(w-4\right)\left(w+2\right)\left(w+7\right)}$$

Pomnožite izraz 4w\left(w-4\right)-\left(2w+5\right)\left(w+2\right).

$$\frac{4w^{2}-16w-2w^{2}-4w-5w-10}{\left(w-4\right)\left(w+2\right)\left(w+7\right)}$$

Kombinirajte slične izraze u 4w^{2}-16w-2w^{2}-4w-5w-10.

$$\frac{2w^{2}-25w-10}{\left(w-4\right)\left(w+2\right)\left(w+7\right)}$$

Proširivanje broja \left(w-4\right)\left(w+2\right)\left(w+7\right).

$$\frac{2w^{2}-25w-10}{w^{3}+5w^{2}-22w-56}$$

Proširi

$$\frac{2w^{2}-25w-10}{\left(w-4\right)\left(w+2\right)\left(w+7\right)}$$

Kratki koraci za rješenje

Rastavite w^{2}+9w+14 na faktore. Rastavite w^{2}+3w-28 na faktore.

$$\frac{4w}{\left(w+2\right)\left(w+7\right)}-\frac{2w+5}{\left(w-4\right)\left(w+7\right)}$$

Da biste zbrojili ili oduzeli izraze, proširite ih da bi imali iste nazivnike. Najmanji zajednički višekratnik brojeva \left(w+2\right)\left(w+7\right) i \left(w-4\right)\left(w+7\right) jest \left(w-4\right)\left(w+2\right)\left(w+7\right). Pomnožite \frac{4w}{\left(w+2\right)\left(w+7\right)} i \frac{w-4}{w-4}. Pomnožite \frac{2w+5}{\left(w-4\right)\left(w+7\right)} i \frac{w+2}{w+2}.

$$\frac{4w\left(w-4\right)}{\left(w-4\right)\left(w+2\right)\left(w+7\right)}-\frac{\left(2w+5\right)\left(w+2\right)}{\left(w-4\right)\left(w+2\right)\left(w+7\right)}$$

Budući da \frac{4w\left(w-4\right)}{\left(w-4\right)\left(w+2\right)\left(w+7\right)} i \frac{\left(2w+5\right)\left(w+2\right)}{\left(w-4\right)\left(w+2\right)\left(w+7\right)} imaju isti nazivnik, oduzmite ih oduzimanje njihovih brojnika.

$$\frac{4w\left(w-4\right)-\left(2w+5\right)\left(w+2\right)}{\left(w-4\right)\left(w+2\right)\left(w+7\right)}$$

Pomnožite izraz 4w\left(w-4\right)-\left(2w+5\right)\left(w+2\right).

$$\frac{4w^{2}-16w-2w^{2}-4w-5w-10}{\left(w-4\right)\left(w+2\right)\left(w+7\right)}$$

Kombinirajte slične izraze u 4w^{2}-16w-2w^{2}-4w-5w-10.

$$\frac{2w^{2}-25w-10}{\left(w-4\right)\left(w+2\right)\left(w+7\right)}$$

Proširivanje broja \left(w-4\right)\left(w+2\right)\left(w+7\right).

$$\frac{2w^{2}-25w-10}{w^{3}+5w^{2}-22w-56}$$