Solve -5x/8x+7-6x^3/3x+1

$$\frac { - 5 x } { 8 x + 7 } - \frac { 6 x ^ { 3 } } { 3 x + 1 }$$

Evaluate

$$-\frac{x\left(48x^{3}+42x^{2}+15x+5\right)}{\left(3x+1\right)\left(8x+7\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 8x+7 and 3x+1 is \left(3x+1\right)\left(8x+7\right). Multiply \frac{-5x}{8x+7} times \frac{3x+1}{3x+1}. Multiply \frac{6x^{3}}{3x+1} times \frac{8x+7}{8x+7}.

$$\frac{-5x\left(3x+1\right)}{\left(3x+1\right)\left(8x+7\right)}-\frac{6x^{3}\left(8x+7\right)}{\left(3x+1\right)\left(8x+7\right)}$$

Since \frac{-5x\left(3x+1\right)}{\left(3x+1\right)\left(8x+7\right)} and \frac{6x^{3}\left(8x+7\right)}{\left(3x+1\right)\left(8x+7\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-5x\left(3x+1\right)-6x^{3}\left(8x+7\right)}{\left(3x+1\right)\left(8x+7\right)}$$

Do the multiplications in -5x\left(3x+1\right)-6x^{3}\left(8x+7\right).

$$\frac{-15x^{2}-5x-48x^{4}-42x^{3}}{\left(3x+1\right)\left(8x+7\right)}$$

Expand \left(3x+1\right)\left(8x+7\right).

$$\frac{-15x^{2}-5x-48x^{4}-42x^{3}}{24x^{2}+29x+7}$$

Factor

$$-\frac{x\left(48x^{3}+42x^{2}+15x+5\right)}{\left(3x+1\right)\left(8x+7\right)}$$