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

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

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{1-x}{1-x}.

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

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

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

Combine like terms in 1-x-1.

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

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

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

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

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

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

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

Cancel out x in both numerator and denominator.

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

Factor the expressions that are not already factored.

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

Extract the negative sign in -1+x.

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

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

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

Expand the expression.

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

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{1-x}{1-x}.

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

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

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

Combine like terms in 1-x-1.

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

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

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

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

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

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

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

Cancel out x in both numerator and denominator.

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

Factor the expressions that are not already factored.

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

Extract the negative sign in -1+x.

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

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

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

Expand the expression.

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