Riješi 2w/w^2-1+w/w-1

$$\frac { 2 w } { w ^ { 2 } - 1 } + \frac { w } { w - 1 }$$

Izračunaj

$$\frac{w\left(w+3\right)}{w^{2}-1}$$

Kratki koraci za rješenje

Rastavite w^{2}-1 na faktore.

$$\frac{2w}{\left(w-1\right)\left(w+1\right)}+\frac{w}{w-1}$$

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

$$\frac{2w}{\left(w-1\right)\left(w+1\right)}+\frac{w\left(w+1\right)}{\left(w-1\right)\left(w+1\right)}$$

Budući da \frac{2w}{\left(w-1\right)\left(w+1\right)} i \frac{w\left(w+1\right)}{\left(w-1\right)\left(w+1\right)} imaju isti nazivnik, zbrojite ih zbrajanjem njihovih brojnika.

$$\frac{2w+w\left(w+1\right)}{\left(w-1\right)\left(w+1\right)}$$

Pomnožite izraz 2w+w\left(w+1\right).

$$\frac{2w+w^{2}+w}{\left(w-1\right)\left(w+1\right)}$$

Kombinirajte slične izraze u 2w+w^{2}+w.

$$\frac{3w+w^{2}}{\left(w-1\right)\left(w+1\right)}$$

Proširivanje broja \left(w-1\right)\left(w+1\right).

$$\frac{3w+w^{2}}{w^{2}-1}$$

Faktor

$$\frac{w\left(w+3\right)}{w^{2}-1}$$