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

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

Evaluate

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

Short Solution Steps

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

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

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

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

Do the multiplications in 2\times 2+xx.

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

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

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

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

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

Do the multiplications in 2\times 2-xx.

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

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

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

Cancel out 2x in both numerator and denominator.

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

Expand

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

Short Solution Steps

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

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

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

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

Do the multiplications in 2\times 2+xx.

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

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

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

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

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

Do the multiplications in 2\times 2-xx.

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

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

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

Cancel out 2x in both numerator and denominator.

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