Solve p/p-1-p/p+1

$$\frac { p } { p - 1 } - \frac { p } { p + 1 }$$

Evaluate

$$\frac{2p}{p^{2}-1}$$

Short Solution Steps

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

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

Since \frac{p\left(p+1\right)}{\left(p-1\right)\left(p+1\right)} and \frac{p\left(p-1\right)}{\left(p-1\right)\left(p+1\right)} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in p\left(p+1\right)-p\left(p-1\right).

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

Combine like terms in p^{2}+p-p^{2}+p.

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

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

$$\frac{2p}{p^{2}-1}$$

Factor

$$\frac{2p}{p^{2}-1}$$