Solve 1-(1-x/x)/(frac{1-x{x})}

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

Evaluate

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

Short Solution Steps

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

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

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

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

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

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

Combine like terms in x-1+x.

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

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

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

Cancel out x in both numerator and denominator.

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

Expand

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

Short Solution Steps

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

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

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

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

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

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

Combine like terms in x-1+x.

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

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

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

Cancel out x in both numerator and denominator.

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