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

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

Evaluate

$$x-2$$

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}.

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

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

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

Do the multiplications in xx-4.

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

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2x and 4 is 4x. Multiply \frac{1}{2x} times \frac{2}{2}. Multiply \frac{1}{4} times \frac{x}{x}.

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

Since \frac{2}{4x} and \frac{x}{4x} have the same denominator, add them by adding their numerators.

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

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

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

Cancel out 4x in both numerator and denominator.

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

Factor the expressions that are not already factored.

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

Cancel out x+2 in both numerator and denominator.

$$x-2$$

Expand

$$x-2$$

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}.

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

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

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

Do the multiplications in xx-4.

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

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2x and 4 is 4x. Multiply \frac{1}{2x} times \frac{2}{2}. Multiply \frac{1}{4} times \frac{x}{x}.

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

Since \frac{2}{4x} and \frac{x}{4x} have the same denominator, add them by adding their numerators.

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

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

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

Cancel out 4x in both numerator and denominator.

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

Factor the expressions that are not already factored.

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

Cancel out x+2 in both numerator and denominator.

$$x-2$$