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

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

Evaluate

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

Short Solution Steps

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

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

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

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

Combine like terms in 1-x+x.

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

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

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

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

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

Combine like terms in 1-x-x.

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

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

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

Cancel out -x+1 in both numerator and denominator.

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

Expand

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

Short Solution Steps

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

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

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

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

Combine like terms in 1-x+x.

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

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

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

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

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

Combine like terms in 1-x-x.

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

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

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

Cancel out -x+1 in both numerator and denominator.

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