Solve 1-4/x/1-frac{x{(1-x)}}

$$\frac { 1 - \frac { 4 } { x } } { 1 - \frac { x } { ( 1 - x ) } }$$

Evaluate

$$\frac{\left(1-x\right)\left(x-4\right)}{x\left(1-2x\right)}$$

Short Solution Steps

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

$$\frac{\frac{x}{x}-\frac{4}{x}}{1-\frac{x}{1-x}}$$

Since \frac{x}{x} and \frac{4}{x} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{x-4}{x}}{1-\frac{x}{1-x}}$$

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

$$\frac{\frac{x-4}{x}}{\frac{1-x}{1-x}-\frac{x}{1-x}}$$

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

$$\frac{\frac{x-4}{x}}{\frac{1-x-x}{1-x}}$$

Combine like terms in 1-x-x.

$$\frac{\frac{x-4}{x}}{\frac{1-2x}{1-x}}$$

Divide \frac{x-4}{x} by \frac{1-2x}{1-x} by multiplying \frac{x-4}{x} by the reciprocal of \frac{1-2x}{1-x}.

$$\frac{\left(x-4\right)\left(1-x\right)}{x\left(1-2x\right)}$$

Apply the distributive property by multiplying each term of x-4 by each term of 1-x.

$$\frac{x-x^{2}-4+4x}{x\left(1-2x\right)}$$

Combine x and 4x to get 5x.

$$\frac{5x-x^{2}-4}{x\left(1-2x\right)}$$

Use the distributive property to multiply x by 1-2x.

$$\frac{5x-x^{2}-4}{x-2x^{2}}$$

Expand

$$\frac{-x^{2}+5x-4}{x\left(1-2x\right)}$$

Short Solution Steps

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

$$\frac{\frac{x}{x}-\frac{4}{x}}{1-\frac{x}{1-x}}$$

Since \frac{x}{x} and \frac{4}{x} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{x-4}{x}}{1-\frac{x}{1-x}}$$

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

$$\frac{\frac{x-4}{x}}{\frac{1-x}{1-x}-\frac{x}{1-x}}$$

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

$$\frac{\frac{x-4}{x}}{\frac{1-x-x}{1-x}}$$

Combine like terms in 1-x-x.

$$\frac{\frac{x-4}{x}}{\frac{1-2x}{1-x}}$$

Divide \frac{x-4}{x} by \frac{1-2x}{1-x} by multiplying \frac{x-4}{x} by the reciprocal of \frac{1-2x}{1-x}.

$$\frac{\left(x-4\right)\left(1-x\right)}{x\left(1-2x\right)}$$

Apply the distributive property by multiplying each term of x-4 by each term of 1-x.

$$\frac{x-x^{2}-4+4x}{x\left(1-2x\right)}$$

Combine x and 4x to get 5x.

$$\frac{5x-x^{2}-4}{x\left(1-2x\right)}$$

Use the distributive property to multiply x by 1-2x.

$$\frac{5x-x^{2}-4}{x-2x^{2}}$$