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

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

Evaluate

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

Short Solution Steps

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

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

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

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

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

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

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

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

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

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

Cancel out x in both numerator and denominator.

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

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

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

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

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

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

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

Combine like terms in x-1-x-1.

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

Expand

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

Short Solution Steps

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

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

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

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

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

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

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

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

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

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

Cancel out x in both numerator and denominator.

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

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

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

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

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

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

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

Combine like terms in x-1-x-1.

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