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

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

Evaluate

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

Short Solution Steps

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

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

Since -\frac{2x}{2x^{2}} and \frac{1}{2x^{2}} have the same denominator, subtract them by subtracting their numerators.

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

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

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

Since \frac{-2x-1}{2x^{2}} and \frac{3x^{2}}{2x^{2}} have the same denominator, add them by adding their numerators.

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

Factor

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