Resolver 2w/w^2-1+w/w-1

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

Calcular

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

Pasos de solución curta

Factoriza w^{2}-1.

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

Para sumar ou restar expresións, expándeas para facer que os seus denominadores sexan iguais. O mínimo común múltiplo de \left(w-1\right)\left(w+1\right) e w-1 é \left(w-1\right)\left(w+1\right). Multiplica \frac{w}{w-1} por \frac{w+1}{w+1}.

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

Dado que \frac{2w}{\left(w-1\right)\left(w+1\right)} e \frac{w\left(w+1\right)}{\left(w-1\right)\left(w+1\right)} teñen o mesmo denominador, súmaos mediante a suma dos seus numeradores.

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

Fai as multiplicacións en 2w+w\left(w+1\right).

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

Combina como termos en 2w+w^{2}+w.

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

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

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

Factorizar

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