Solve 1/6x+1/3x^2-1/2x^3

$$\frac { 1 } { 6 x } + \frac { 1 } { 3 x ^ { 2 } } - \frac { 1 } { 2 x ^ { 3 } }$$

Evaluate

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 6x and 3x^{2} is 6x^{2}. Multiply \frac{1}{6x} times \frac{x}{x}. Multiply \frac{1}{3x^{2}} times \frac{2}{2}.

$$\frac{x}{6x^{2}}+\frac{2}{6x^{2}}-\frac{1}{2x^{3}}$$

Since \frac{x}{6x^{2}} and \frac{2}{6x^{2}} have the same denominator, add them by adding their numerators.

$$\frac{x+2}{6x^{2}}-\frac{1}{2x^{3}}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 6x^{2} and 2x^{3} is 6x^{3}. Multiply \frac{x+2}{6x^{2}} times \frac{x}{x}. Multiply \frac{1}{2x^{3}} times \frac{3}{3}.

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

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

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

Do the multiplications in \left(x+2\right)x-3.

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

Factor

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