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

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

Evaluate

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

Short Solution Steps

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

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

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

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

Combine like terms in x-1+1.

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

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

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

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

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

Multiply \frac{x}{x-1} times \frac{1-x^{2}}{x^{2}} by multiplying numerator times numerator and denominator times denominator.

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

Cancel out x in both numerator and denominator.

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

Factor the expressions that are not already factored.

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

Cancel out x-1 in both numerator and denominator.

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

Expand

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

Short Solution Steps

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

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

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

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

Combine like terms in x-1+1.

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

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

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

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

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

Multiply \frac{x}{x-1} times \frac{1-x^{2}}{x^{2}} by multiplying numerator times numerator and denominator times denominator.

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

Cancel out x in both numerator and denominator.

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

Factor the expressions that are not already factored.

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

Cancel out x-1 in both numerator and denominator.

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