Rešite 2w/w^2-1+w/w-1

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

Ovrednoti

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

Kratka navodila za rešitev

Faktorizirajte w^{2}-1.

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

Če želite prišteti ali odšteti izraze, jih razširite na skupne imenovalce. Najmanjši skupni mnogokratnik \left(w-1\right)\left(w+1\right) in w-1 je \left(w-1\right)\left(w+1\right). Pomnožite \frac{w}{w-1} s/z \frac{w+1}{w+1}.

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

\frac{2w}{\left(w-1\right)\left(w+1\right)} in \frac{w\left(w+1\right)}{\left(w-1\right)\left(w+1\right)} imata isti imenovalec, zato ju seštejte tako, da seštejete njuna števca.

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

Izvedi množenje v 2w+w\left(w+1\right).

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

Združite podobne člene v 2w+w^{2}+w.

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

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

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

Faktoriziraj

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