Solve (x^3-x):(1/x-1)

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

Evaluate

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

Short Solution Steps

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

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

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

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

Divide x^{3}-x by \frac{1-x}{x} by multiplying x^{3}-x by the reciprocal of \frac{1-x}{x}.

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

Factor the expressions that are not already factored.

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

Extract the negative sign in -1+x.

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

Cancel out -x+1 in both numerator and denominator.

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

Expand the expression.

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

Expand

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

Short Solution Steps

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

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

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

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

Divide x^{3}-x by \frac{1-x}{x} by multiplying x^{3}-x by the reciprocal of \frac{1-x}{x}.

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

Factor the expressions that are not already factored.

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

Extract the negative sign in -1+x.

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

Cancel out -x+1 in both numerator and denominator.

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

Expand the expression.

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