Solve 5m^3-13m^2+15m+7divleft(4+mright)

$$5 { m }^{ 3 } -13 { m }^{ 2 } +15m+7 \div \left( 4+m \right)$$

Evaluate

$$\frac{5m^{4}+7m^{3}-37m^{2}+60m+7}{m+4}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 5m^{3}-13m^{2}+15m times \frac{4+m}{4+m}.

$$\frac{\left(5m^{3}-13m^{2}+15m\right)\left(4+m\right)}{4+m}+\frac{7}{4+m}$$

Since \frac{\left(5m^{3}-13m^{2}+15m\right)\left(4+m\right)}{4+m} and \frac{7}{4+m} have the same denominator, add them by adding their numerators.

$$\frac{\left(5m^{3}-13m^{2}+15m\right)\left(4+m\right)+7}{4+m}$$

Do the multiplications in \left(5m^{3}-13m^{2}+15m\right)\left(4+m\right)+7.

$$\frac{20m^{3}+5m^{4}-52m^{2}-13m^{3}+60m+15m^{2}+7}{4+m}$$

Combine like terms in 20m^{3}+5m^{4}-52m^{2}-13m^{3}+60m+15m^{2}+7.

$$\frac{7m^{3}+5m^{4}-37m^{2}+60m+7}{4+m}$$

Differentiate w.r.t. m

$$\frac{15m^{4}+94m^{3}+47m^{2}-296m+233}{\left(m+4\right)^{2}}$$