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

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

Evaluate

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

Short Solution Steps

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

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

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

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

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

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

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

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

Do the multiplications in 1-x^{2}+x^{2}x^{3}.

$$\frac{1-x^{2}+x^{5}}{x^{3}}$$

Factor

$$\frac{x^{5}-x^{2}+1}{x^{3}}$$