Solve 3m^4/3m+2-4m^2/5m+2

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

Evaluate

$$\frac{m^{2}\left(15m^{3}+6m^{2}-12m-8\right)}{\left(3m+2\right)\left(5m+2\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3m+2 and 5m+2 is \left(3m+2\right)\left(5m+2\right). Multiply \frac{3m^{4}}{3m+2} times \frac{5m+2}{5m+2}. Multiply \frac{4m^{2}}{5m+2} times \frac{3m+2}{3m+2}.

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

Since \frac{3m^{4}\left(5m+2\right)}{\left(3m+2\right)\left(5m+2\right)} and \frac{4m^{2}\left(3m+2\right)}{\left(3m+2\right)\left(5m+2\right)} have the same denominator, subtract them by subtracting their numerators.

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

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

$$\frac{15m^{5}+6m^{4}-12m^{3}-8m^{2}}{\left(3m+2\right)\left(5m+2\right)}$$

Expand \left(3m+2\right)\left(5m+2\right).

$$\frac{15m^{5}+6m^{4}-12m^{3}-8m^{2}}{15m^{2}+16m+4}$$

Factor

$$\frac{m^{2}\left(15m^{3}+6m^{2}-12m-8\right)}{\left(3m+2\right)\left(5m+2\right)}$$