Solve 2/3x^3-2/x-3/2

$$\frac{ 2 }{ 3 { x }^{ 3 } } - \frac{ 2 }{ x } - \frac{ 3 }{ 2 }$$

Evaluate

$$-\frac{3}{2}-\frac{2}{x}+\frac{2}{3x^{3}}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3x^{3} and x is 3x^{3}. Multiply \frac{2}{x} times \frac{3x^{2}}{3x^{2}}.

$$\frac{2}{3x^{3}}-\frac{2\times 3x^{2}}{3x^{3}}-\frac{3}{2}$$

Since \frac{2}{3x^{3}} and \frac{2\times 3x^{2}}{3x^{3}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2-2\times 3x^{2}}{3x^{3}}-\frac{3}{2}$$

Do the multiplications in 2-2\times 3x^{2}.

$$\frac{2-6x^{2}}{3x^{3}}-\frac{3}{2}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3x^{3} and 2 is 6x^{3}. Multiply \frac{2-6x^{2}}{3x^{3}} times \frac{2}{2}. Multiply \frac{3}{2} times \frac{3x^{3}}{3x^{3}}.

$$\frac{2\left(2-6x^{2}\right)}{6x^{3}}-\frac{3\times 3x^{3}}{6x^{3}}$$

Since \frac{2\left(2-6x^{2}\right)}{6x^{3}} and \frac{3\times 3x^{3}}{6x^{3}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2\left(2-6x^{2}\right)-3\times 3x^{3}}{6x^{3}}$$

Do the multiplications in 2\left(2-6x^{2}\right)-3\times 3x^{3}.

$$\frac{4-12x^{2}-9x^{3}}{6x^{3}}$$

Factor

$$-\frac{\frac{1}{6}\left(9x^{3}+12x^{2}-4\right)}{x^{3}}$$