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

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

Evaluate

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

Short Solution Steps

Factor the expressions that are not already factored in \frac{\left(x-1\right)^{3}}{x^{2}-1}.

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

Cancel out x-1 in both numerator and denominator.

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

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

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

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

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

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

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

Combine like terms in x^{2}-2x+1-x-1.

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

Expand

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

Short Solution Steps

Factor the expressions that are not already factored in \frac{\left(x-1\right)^{3}}{x^{2}-1}.

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

Cancel out x-1 in both numerator and denominator.

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

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

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

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

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

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

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

Combine like terms in x^{2}-2x+1-x-1.

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