Solve 5/m+2-5/m-6

$$\frac { 5 } { m + 2 } - \frac { 5 } { m - 6 }$$

Evaluate

$$-\frac{40}{\left(m-6\right)\left(m+2\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of m+2 and m-6 is \left(m-6\right)\left(m+2\right). Multiply \frac{5}{m+2} times \frac{m-6}{m-6}. Multiply \frac{5}{m-6} times \frac{m+2}{m+2}.

$$\frac{5\left(m-6\right)}{\left(m-6\right)\left(m+2\right)}-\frac{5\left(m+2\right)}{\left(m-6\right)\left(m+2\right)}$$

Since \frac{5\left(m-6\right)}{\left(m-6\right)\left(m+2\right)} and \frac{5\left(m+2\right)}{\left(m-6\right)\left(m+2\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5\left(m-6\right)-5\left(m+2\right)}{\left(m-6\right)\left(m+2\right)}$$

Do the multiplications in 5\left(m-6\right)-5\left(m+2\right).

$$\frac{5m-30-5m-10}{\left(m-6\right)\left(m+2\right)}$$

Combine like terms in 5m-30-5m-10.

$$\frac{-40}{\left(m-6\right)\left(m+2\right)}$$

Expand \left(m-6\right)\left(m+2\right).

$$\frac{-40}{m^{2}-4m-12}$$

Factor

$$-\frac{40}{\left(m-6\right)\left(m+2\right)}$$