Solve m^4/(5m+4)(1-2m)-3m/(3m-13)(1-2m)

$$\frac { m ^ { 4 } } { ( 5 m + 4 ) ( 1 - 2 m ) } - \frac { 3 m } { ( 3 m - 13 ) ( 1 - 2 m ) }$$

Evaluate

$$\frac{m\left(3m^{4}-13m^{3}-15m-12\right)}{\left(1-2m\right)\left(3m-13\right)\left(5m+4\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(5m+4\right)\left(1-2m\right) and \left(3m-13\right)\left(1-2m\right) is \left(3m-13\right)\left(-2m+1\right)\left(5m+4\right). Multiply \frac{m^{4}}{\left(5m+4\right)\left(1-2m\right)} times \frac{3m-13}{3m-13}. Multiply \frac{3m}{\left(3m-13\right)\left(1-2m\right)} times \frac{5m+4}{5m+4}.

$$\frac{m^{4}\left(3m-13\right)}{\left(3m-13\right)\left(-2m+1\right)\left(5m+4\right)}-\frac{3m\left(5m+4\right)}{\left(3m-13\right)\left(-2m+1\right)\left(5m+4\right)}$$

Since \frac{m^{4}\left(3m-13\right)}{\left(3m-13\right)\left(-2m+1\right)\left(5m+4\right)} and \frac{3m\left(5m+4\right)}{\left(3m-13\right)\left(-2m+1\right)\left(5m+4\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{m^{4}\left(3m-13\right)-3m\left(5m+4\right)}{\left(3m-13\right)\left(-2m+1\right)\left(5m+4\right)}$$

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

$$\frac{3m^{5}-13m^{4}-15m^{2}-12m}{\left(3m-13\right)\left(-2m+1\right)\left(5m+4\right)}$$

Expand \left(3m-13\right)\left(-2m+1\right)\left(5m+4\right).

$$\frac{3m^{5}-13m^{4}-15m^{2}-12m}{-30m^{3}+121m^{2}+51m-52}$$

Expand

$$\frac{3m^{5}-13m^{4}-15m^{2}-12m}{\left(1-2m\right)\left(3m-13\right)\left(5m+4\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(5m+4\right)\left(1-2m\right) and \left(3m-13\right)\left(1-2m\right) is \left(3m-13\right)\left(-2m+1\right)\left(5m+4\right). Multiply \frac{m^{4}}{\left(5m+4\right)\left(1-2m\right)} times \frac{3m-13}{3m-13}. Multiply \frac{3m}{\left(3m-13\right)\left(1-2m\right)} times \frac{5m+4}{5m+4}.

$$\frac{m^{4}\left(3m-13\right)}{\left(3m-13\right)\left(-2m+1\right)\left(5m+4\right)}-\frac{3m\left(5m+4\right)}{\left(3m-13\right)\left(-2m+1\right)\left(5m+4\right)}$$

Since \frac{m^{4}\left(3m-13\right)}{\left(3m-13\right)\left(-2m+1\right)\left(5m+4\right)} and \frac{3m\left(5m+4\right)}{\left(3m-13\right)\left(-2m+1\right)\left(5m+4\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{m^{4}\left(3m-13\right)-3m\left(5m+4\right)}{\left(3m-13\right)\left(-2m+1\right)\left(5m+4\right)}$$

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

$$\frac{3m^{5}-13m^{4}-15m^{2}-12m}{\left(3m-13\right)\left(-2m+1\right)\left(5m+4\right)}$$

Expand \left(3m-13\right)\left(-2m+1\right)\left(5m+4\right).

$$\frac{3m^{5}-13m^{4}-15m^{2}-12m}{-30m^{3}+121m^{2}+51m-52}$$