Solve f(x)=1/x^3+x^2/2+x

$$f ( x ) = \frac { 1 } { x ^ { 3 } } + \frac { x ^ { 2 } } { 2 } + x$$

Evaluate

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

Short Solution Steps

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

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

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

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

Do the multiplications in 2+x^{2}x^{3}.

$$\frac{2+x^{5}}{2x^{3}}+x$$

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

$$\frac{2+x^{5}}{2x^{3}}+\frac{x\times 2x^{3}}{2x^{3}}$$

Since \frac{2+x^{5}}{2x^{3}} and \frac{x\times 2x^{3}}{2x^{3}} have the same denominator, add them by adding their numerators.

$$\frac{2+x^{5}+x\times 2x^{3}}{2x^{3}}$$

Do the multiplications in 2+x^{5}+x\times 2x^{3}.

$$\frac{2+x^{5}+2x^{4}}{2x^{3}}$$

Factor

$$\frac{x^{5}+2x^{4}+2}{2x^{3}}$$