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

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

Evaluate

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

Short Solution Steps

Anything divided by one gives itself.

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

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

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

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

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

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

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

Anything divided by one gives itself.

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

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

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

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

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

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

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

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

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

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

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

Cancel out x-1 in both numerator and denominator.

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

Factor the expressions that are not already factored.

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

Cancel out x+1 in both numerator and denominator.

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

Expand

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

Short Solution Steps

Anything divided by one gives itself.

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

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

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

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

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

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

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

Anything divided by one gives itself.

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

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

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

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

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

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

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

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

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

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

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

Cancel out x-1 in both numerator and denominator.

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

Factor the expressions that are not already factored.

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

Cancel out x+1 in both numerator and denominator.

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