Solve 1/5-1/x/frac{1{1}-1/2}=

$$\frac { \frac { 1 } { 5 } - \frac { 1 } { x } } { \frac { 1 } { 1 } - \frac { 1 } { 2 } } =$$

Evaluate

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

Short Solution Steps

Divide 1 by 1 to get 1.

$$\frac{\frac{1}{5}-\frac{1}{x}}{1-\frac{1}{2}}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 5 and x is 5x. Multiply \frac{1}{5} times \frac{x}{x}. Multiply \frac{1}{x} times \frac{5}{5}.

$$\frac{\frac{x}{5x}-\frac{5}{5x}}{1-\frac{1}{2}}$$

Since \frac{x}{5x} and \frac{5}{5x} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{x-5}{5x}}{1-\frac{1}{2}}$$

Convert 1 to fraction \frac{2}{2}.

$$\frac{\frac{x-5}{5x}}{\frac{2}{2}-\frac{1}{2}}$$

Since \frac{2}{2} and \frac{1}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{x-5}{5x}}{\frac{2-1}{2}}$$

Subtract 1 from 2 to get 1.

$$\frac{\frac{x-5}{5x}}{\frac{1}{2}}$$

Divide \frac{x-5}{5x} by \frac{1}{2} by multiplying \frac{x-5}{5x} by the reciprocal of \frac{1}{2}.

$$\frac{\left(x-5\right)\times 2}{5x}$$

Use the distributive property to multiply x-5 by 2.

$$\frac{2x-10}{5x}$$

Expand

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

Short Solution Steps

Divide 1 by 1 to get 1.

$$\frac{\frac{1}{5}-\frac{1}{x}}{1-\frac{1}{2}}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 5 and x is 5x. Multiply \frac{1}{5} times \frac{x}{x}. Multiply \frac{1}{x} times \frac{5}{5}.

$$\frac{\frac{x}{5x}-\frac{5}{5x}}{1-\frac{1}{2}}$$

Since \frac{x}{5x} and \frac{5}{5x} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{x-5}{5x}}{1-\frac{1}{2}}$$

Convert 1 to fraction \frac{2}{2}.

$$\frac{\frac{x-5}{5x}}{\frac{2}{2}-\frac{1}{2}}$$

Since \frac{2}{2} and \frac{1}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{x-5}{5x}}{\frac{2-1}{2}}$$

Subtract 1 from 2 to get 1.

$$\frac{\frac{x-5}{5x}}{\frac{1}{2}}$$

Divide \frac{x-5}{5x} by \frac{1}{2} by multiplying \frac{x-5}{5x} by the reciprocal of \frac{1}{2}.

$$\frac{\left(x-5\right)\times 2}{5x}$$

Use the distributive property to multiply x-5 by 2.

$$\frac{2x-10}{5x}$$