Solve 4/z+5-4/z-5

$$\frac { 4 } { z + 5 } - \frac { 4 } { z - 5 }$$

Evaluate

$$-\frac{40}{z^{2}-25}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of z+5 and z-5 is \left(z-5\right)\left(z+5\right). Multiply \frac{4}{z+5} times \frac{z-5}{z-5}. Multiply \frac{4}{z-5} times \frac{z+5}{z+5}.

$$\frac{4\left(z-5\right)}{\left(z-5\right)\left(z+5\right)}-\frac{4\left(z+5\right)}{\left(z-5\right)\left(z+5\right)}$$

Since \frac{4\left(z-5\right)}{\left(z-5\right)\left(z+5\right)} and \frac{4\left(z+5\right)}{\left(z-5\right)\left(z+5\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4\left(z-5\right)-4\left(z+5\right)}{\left(z-5\right)\left(z+5\right)}$$

Do the multiplications in 4\left(z-5\right)-4\left(z+5\right).

$$\frac{4z-20-4z-20}{\left(z-5\right)\left(z+5\right)}$$

Combine like terms in 4z-20-4z-20.

$$\frac{-40}{\left(z-5\right)\left(z+5\right)}$$

Expand \left(z-5\right)\left(z+5\right).

$$\frac{-40}{z^{2}-25}$$

Factor

$$-\frac{40}{z^{2}-25}$$