Solve 5m/m^2-81+m/m-9

$$\frac { 5 m } { m ^ { 2 } - 81 } + \frac { m } { m - 9 }$$

Evaluate

$$\frac{m\left(m+14\right)}{m^{2}-81}$$

Short Solution Steps

Factor m^{2}-81.

$$\frac{5m}{\left(m-9\right)\left(m+9\right)}+\frac{m}{m-9}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(m-9\right)\left(m+9\right) and m-9 is \left(m-9\right)\left(m+9\right). Multiply \frac{m}{m-9} times \frac{m+9}{m+9}.

$$\frac{5m}{\left(m-9\right)\left(m+9\right)}+\frac{m\left(m+9\right)}{\left(m-9\right)\left(m+9\right)}$$

Since \frac{5m}{\left(m-9\right)\left(m+9\right)} and \frac{m\left(m+9\right)}{\left(m-9\right)\left(m+9\right)} have the same denominator, add them by adding their numerators.

$$\frac{5m+m\left(m+9\right)}{\left(m-9\right)\left(m+9\right)}$$

Do the multiplications in 5m+m\left(m+9\right).

$$\frac{5m+m^{2}+9m}{\left(m-9\right)\left(m+9\right)}$$

Combine like terms in 5m+m^{2}+9m.

$$\frac{14m+m^{2}}{\left(m-9\right)\left(m+9\right)}$$

Expand \left(m-9\right)\left(m+9\right).

$$\frac{14m+m^{2}}{m^{2}-81}$$

Factor

$$\frac{m\left(m+14\right)}{m^{2}-81}$$