Riješi 2w/w^2-1+w/w-1

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

Procijeni

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

Kratki koraci rješenja

Faktorirajte w^{2}-1.

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

Da biste izvršili zbrajanje ili oduzimanje izraza, rastavite ih kako bi im nazivnici bili isti. Najmanji zajednički množilac brojeva \left(w-1\right)\left(w+1\right) i w-1 je \left(w-1\right)\left(w+1\right). Pomnožite \frac{w}{w-1} i \frac{w+1}{w+1}.

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

Pošto \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 imenilac, saberite ih tako što ćete sabrati njihove brojioce.

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

Izvršite množenja u 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.

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

Proširite \left(w-1\right)\left(w+1\right).

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

Faktor

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