Solve 19m+3m^3/14m-3-12m^2+3m/14-3

$$\frac { 19 m + 3 m ^ { 3 } } { 14 m - 3 } - \frac { 12 m ^ { 2 } + 3 m } { 14 - 3 }$$

Evaluate

$$\frac{m\left(218-6m-135m^{2}\right)}{11\left(14m-3\right)}$$

Short Solution Steps

Subtract 3 from 14 to get 11.

$$\frac{19m+3m^{3}}{14m-3}-\frac{12m^{2}+3m}{11}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 14m-3 and 11 is 11\left(14m-3\right). Multiply \frac{19m+3m^{3}}{14m-3} times \frac{11}{11}. Multiply \frac{12m^{2}+3m}{11} times \frac{14m-3}{14m-3}.

$$\frac{11\left(19m+3m^{3}\right)}{11\left(14m-3\right)}-\frac{\left(12m^{2}+3m\right)\left(14m-3\right)}{11\left(14m-3\right)}$$

Since \frac{11\left(19m+3m^{3}\right)}{11\left(14m-3\right)} and \frac{\left(12m^{2}+3m\right)\left(14m-3\right)}{11\left(14m-3\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{11\left(19m+3m^{3}\right)-\left(12m^{2}+3m\right)\left(14m-3\right)}{11\left(14m-3\right)}$$

Do the multiplications in 11\left(19m+3m^{3}\right)-\left(12m^{2}+3m\right)\left(14m-3\right).

$$\frac{209m+33m^{3}-168m^{3}+36m^{2}-42m^{2}+9m}{11\left(14m-3\right)}$$

Combine like terms in 209m+33m^{3}-168m^{3}+36m^{2}-42m^{2}+9m.

$$\frac{218m-135m^{3}-6m^{2}}{11\left(14m-3\right)}$$

Expand 11\left(14m-3\right).

$$\frac{218m-135m^{3}-6m^{2}}{154m-33}$$

Expand

$$-\frac{135m^{3}+6m^{2}-218m}{11\left(14m-3\right)}$$

Short Solution Steps

Subtract 3 from 14 to get 11.

$$\frac{19m+3m^{3}}{14m-3}-\frac{12m^{2}+3m}{11}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 14m-3 and 11 is 11\left(14m-3\right). Multiply \frac{19m+3m^{3}}{14m-3} times \frac{11}{11}. Multiply \frac{12m^{2}+3m}{11} times \frac{14m-3}{14m-3}.

$$\frac{11\left(19m+3m^{3}\right)}{11\left(14m-3\right)}-\frac{\left(12m^{2}+3m\right)\left(14m-3\right)}{11\left(14m-3\right)}$$

Since \frac{11\left(19m+3m^{3}\right)}{11\left(14m-3\right)} and \frac{\left(12m^{2}+3m\right)\left(14m-3\right)}{11\left(14m-3\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{11\left(19m+3m^{3}\right)-\left(12m^{2}+3m\right)\left(14m-3\right)}{11\left(14m-3\right)}$$

Do the multiplications in 11\left(19m+3m^{3}\right)-\left(12m^{2}+3m\right)\left(14m-3\right).

$$\frac{209m+33m^{3}-168m^{3}+36m^{2}-42m^{2}+9m}{11\left(14m-3\right)}$$

Combine like terms in 209m+33m^{3}-168m^{3}+36m^{2}-42m^{2}+9m.

$$\frac{218m-135m^{3}-6m^{2}}{11\left(14m-3\right)}$$

Expand 11\left(14m-3\right).

$$\frac{218m-135m^{3}-6m^{2}}{154m-33}$$