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

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

Evaluate

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

Short Solution Steps

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

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

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

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

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

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

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

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

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

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

Divide \frac{x^{2}-2x+1}{x^{2}} by \frac{x^{2}-1}{x^{2}} by multiplying \frac{x^{2}-2x+1}{x^{2}} by the reciprocal of \frac{x^{2}-1}{x^{2}}.

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

Cancel out x^{2} in both numerator and denominator.

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

Factor the expressions that are not already factored.

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

Cancel out x-1 in both numerator and denominator.

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

Expand

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

Short Solution Steps

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

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

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

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

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

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

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

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

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

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

Divide \frac{x^{2}-2x+1}{x^{2}} by \frac{x^{2}-1}{x^{2}} by multiplying \frac{x^{2}-2x+1}{x^{2}} by the reciprocal of \frac{x^{2}-1}{x^{2}}.

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

Cancel out x^{2} in both numerator and denominator.

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

Factor the expressions that are not already factored.

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

Cancel out x-1 in both numerator and denominator.

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