Solve x/4-1/x/1-frac{2{x}}

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

Evaluate

$$\frac{x+2}{4}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4 and x is 4x. Multiply \frac{x}{4} times \frac{x}{x}. Multiply \frac{1}{x} times \frac{4}{4}.

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

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

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

Do the multiplications in xx-4.

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

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

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

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

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

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

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

Cancel out x in both numerator and denominator.

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

Factor the expressions that are not already factored.

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

Cancel out x-2 in both numerator and denominator.

$$\frac{x+2}{4}$$

Expand

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4 and x is 4x. Multiply \frac{x}{4} times \frac{x}{x}. Multiply \frac{1}{x} times \frac{4}{4}.

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

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

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

Do the multiplications in xx-4.

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

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

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

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

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

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

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

Cancel out x in both numerator and denominator.

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

Factor the expressions that are not already factored.

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

Cancel out x-2 in both numerator and denominator.

$$\frac{x+2}{4}$$