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

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

Evaluate

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

Short Solution Steps

Factor the expressions that are not already factored in \frac{x^{2}}{x+x^{-1}}.

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

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply x^{3} times \frac{x^{2}+1}{x^{2}+1}.

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

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

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

Do the multiplications in x^{3}\left(x^{2}+1\right)-x^{3}.

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

Combine like terms in x^{5}+x^{3}-x^{3}.

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

Factor

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