Solve 4/m+3-9m/m+6

$$\frac { 4 } { m + 3 } - \frac { 9 m } { m + 6 }$$

Evaluate

$$\frac{24-23m-9m^{2}}{\left(m+3\right)\left(m+6\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of m+3 and m+6 is \left(m+3\right)\left(m+6\right). Multiply \frac{4}{m+3} times \frac{m+6}{m+6}. Multiply \frac{9m}{m+6} times \frac{m+3}{m+3}.

$$\frac{4\left(m+6\right)}{\left(m+3\right)\left(m+6\right)}-\frac{9m\left(m+3\right)}{\left(m+3\right)\left(m+6\right)}$$

Since \frac{4\left(m+6\right)}{\left(m+3\right)\left(m+6\right)} and \frac{9m\left(m+3\right)}{\left(m+3\right)\left(m+6\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4\left(m+6\right)-9m\left(m+3\right)}{\left(m+3\right)\left(m+6\right)}$$

Do the multiplications in 4\left(m+6\right)-9m\left(m+3\right).

$$\frac{4m+24-9m^{2}-27m}{\left(m+3\right)\left(m+6\right)}$$

Combine like terms in 4m+24-9m^{2}-27m.

$$\frac{-23m+24-9m^{2}}{\left(m+3\right)\left(m+6\right)}$$

Expand \left(m+3\right)\left(m+6\right).

$$\frac{-23m+24-9m^{2}}{m^{2}+9m+18}$$

Differentiate w.r.t. m

$$-\frac{2\left(29m^{2}+186m+315\right)}{\left(\left(m+3\right)\left(m+6\right)\right)^{2}}$$