Solve (x+x/x-1):(x-x/x-1)

$$( x + \frac { x } { x - 1 } ) : ( x - \frac { x } { x - 1 } )$$

Evaluate

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

Short Solution Steps

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Cancel out x-1 in both numerator and denominator.

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

Factor the expressions that are not already factored.

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

Cancel out x in both numerator and denominator.

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

Expand

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

Short Solution Steps

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Cancel out x-1 in both numerator and denominator.

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

Factor the expressions that are not already factored.

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

Cancel out x in both numerator and denominator.

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