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

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

Evaluate

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

Solution Steps

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

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

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2 and x is 2x. Multiply \frac{1}{2} times \frac{x}{x}. Multiply \frac{1}{x} times \frac{2}{2}.

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

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

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

Express \frac{x-2}{2x}\times 2 as a single fraction.

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

Cancel out 2 in both numerator and denominator.

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

Express \frac{\frac{x-2}{x}}{2-x} as a single fraction.

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

Extract the negative sign in x-2.

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

Cancel out -x+2 in both numerator and denominator.

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

Expand

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

Solution Steps

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

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

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2 and x is 2x. Multiply \frac{1}{2} times \frac{x}{x}. Multiply \frac{1}{x} times \frac{2}{2}.

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

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

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

Express \frac{x-2}{2x}\times 2 as a single fraction.

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

Cancel out 2 in both numerator and denominator.

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

Express \frac{\frac{x-2}{x}}{2-x} as a single fraction.

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

Extract the negative sign in x-2.

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

Cancel out -x+2 in both numerator and denominator.

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