Solve p/p+2-p/p-2

$$\frac { p } { p + 2 } - \frac { p } { p - 2 }$$

Evaluate

$$-\frac{4p}{p^{2}-4}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of p+2 and p-2 is \left(p-2\right)\left(p+2\right). Multiply \frac{p}{p+2} times \frac{p-2}{p-2}. Multiply \frac{p}{p-2} times \frac{p+2}{p+2}.

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

Since \frac{p\left(p-2\right)}{\left(p-2\right)\left(p+2\right)} and \frac{p\left(p+2\right)}{\left(p-2\right)\left(p+2\right)} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in p\left(p-2\right)-p\left(p+2\right).

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

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

$$\frac{-4p}{\left(p-2\right)\left(p+2\right)}$$

Expand \left(p-2\right)\left(p+2\right).

$$\frac{-4p}{p^{2}-4}$$

Factor

$$-\frac{4p}{p^{2}-4}$$