Solve 2w/w^2-1+w/w-1

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

Evaluate

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

Short Solution Steps

Factor w^{2}-1.

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

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(w-1\right)\left(w+1\right) and w-1 is \left(w-1\right)\left(w+1\right). Multiply \frac{w}{w-1} times \frac{w+1}{w+1}.

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

Since \frac{2w}{\left(w-1\right)\left(w+1\right)} and \frac{w\left(w+1\right)}{\left(w-1\right)\left(w+1\right)} have the same denominator, add them by adding their numerators.

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

Do the multiplications in 2w+w\left(w+1\right).

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

Combine like terms in 2w+w^{2}+w.

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

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

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

Factor

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