Solve 3/x-x/2+5

$$\frac { 3 } { x } - \frac { x } { 2 } + 5$$

Evaluate

$$-\frac{x}{2}+5+\frac{3}{x}$$

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{3}{x} times \frac{2}{2}. Multiply \frac{x}{2} times \frac{x}{x}.

$$\frac{3\times 2}{2x}-\frac{xx}{2x}+5$$

Since \frac{3\times 2}{2x} and \frac{xx}{2x} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3\times 2-xx}{2x}+5$$

Do the multiplications in 3\times 2-xx.

$$\frac{6-x^{2}}{2x}+5$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 5 times \frac{2x}{2x}.

$$\frac{6-x^{2}}{2x}+\frac{5\times 2x}{2x}$$

Since \frac{6-x^{2}}{2x} and \frac{5\times 2x}{2x} have the same denominator, add them by adding their numerators.

$$\frac{6-x^{2}+5\times 2x}{2x}$$

Do the multiplications in 6-x^{2}+5\times 2x.

$$\frac{6-x^{2}+10x}{2x}$$

Factor

$$-\frac{\frac{1}{2}\left(x-\left(5-\sqrt{31}\right)\right)\left(x-\left(\sqrt{31}+5\right)\right)}{x}$$