Solve x-2x/x-1/x-frac{x{-x-1}}

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

Evaluate

$$\frac{\left(x-3\right)\left(x+1\right)}{\left(x-1\right)\left(x+2\right)}$$

Short Solution Steps

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Divide \frac{x^{2}-3x}{x-1} by \frac{-x^{2}-2x}{-x-1} by multiplying \frac{x^{2}-3x}{x-1} by the reciprocal of \frac{-x^{2}-2x}{-x-1}.

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

Factor the expressions that are not already factored.

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

Cancel out x in both numerator and denominator.

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

Expand the expression.

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

Expand

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

Short Solution Steps

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Divide \frac{x^{2}-3x}{x-1} by \frac{-x^{2}-2x}{-x-1} by multiplying \frac{x^{2}-3x}{x-1} by the reciprocal of \frac{-x^{2}-2x}{-x-1}.

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

Factor the expressions that are not already factored.

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

Cancel out x in both numerator and denominator.

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

Expand the expression.

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