Solve 1/2(x+2/x)-x

$$\frac{ 1 }{ 2 } (x+ \frac{ 2 }{ x } )-x$$

Evaluate

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

Short Solution Steps

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

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

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

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

Do the multiplications in xx+2.

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

Multiply \frac{1}{2} times \frac{x^{2}+2}{x} by multiplying numerator times numerator and denominator times denominator.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply x times \frac{2x}{2x}.

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

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

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

Do the multiplications in x^{2}+2-x\times 2x.

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

Combine like terms in x^{2}+2-2x^{2}.

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

Expand

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

Short Solution Steps

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

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

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

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

Do the multiplications in xx+2.

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

Multiply \frac{1}{2} times \frac{x^{2}+2}{x} by multiplying numerator times numerator and denominator times denominator.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply x times \frac{2x}{2x}.

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

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

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

Do the multiplications in x^{2}+2-x\times 2x.

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

Combine like terms in x^{2}+2-2x^{2}.

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