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

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

Evaluate

$$x-1$$

Short Solution Steps

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

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

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

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

Do the multiplications in xx-\left(2x-1\right).

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

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

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

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

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

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

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

Cancel out x in both numerator and denominator.

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

Factor the expressions that are not already factored.

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

Cancel out x-1 in both numerator and denominator.

$$x-1$$

Expand

$$x-1$$

Short Solution Steps

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

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

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

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

Do the multiplications in xx-\left(2x-1\right).

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

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

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

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

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

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

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

Cancel out x in both numerator and denominator.

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

Factor the expressions that are not already factored.

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

Cancel out x-1 in both numerator and denominator.

$$x-1$$