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

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

Evaluate

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

Short Solution Steps

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

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

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

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

To add or subtract expressions, expand them to make their denominators the same. Multiply x^{3}+3x^{2}+3x times \frac{2x}{2x}.

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

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

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

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

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

Factor

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