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

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

Evaluate

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

Short Solution Steps

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

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

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

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

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

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

Express \frac{x^{3}-1}{x}\left(x^{3}+2x\right) as a single fraction.

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

Factor the expressions that are not already factored.

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

Cancel out x in both numerator and denominator.

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

Expand the expression.

$$x^{5}+2x^{3}-x^{2}-2$$

Expand

$$x^{5}+2x^{3}-x^{2}-2$$

Short Solution Steps

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

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

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

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

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

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

Express \frac{x^{3}-1}{x}\left(x^{3}+2x\right) as a single fraction.

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

Factor the expressions that are not already factored.

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

Cancel out x in both numerator and denominator.

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

Expand the expression.

$$x^{5}+2x^{3}-x^{2}-2$$