Solve (x/2+2/x)div(6/x)

$$( \frac { x } { 2 } + \frac { 2 } { x } ) \div ( \frac { 6 } { x } )$$

Evaluate

$$\frac{x^{2}}{12}+\frac{1}{3}$$

Short Solution Steps

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

$$\frac{\frac{xx}{2x}+\frac{2\times 2}{2x}}{\frac{6}{x}}$$

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

$$\frac{\frac{xx+2\times 2}{2x}}{\frac{6}{x}}$$

Do the multiplications in xx+2\times 2.

$$\frac{\frac{x^{2}+4}{2x}}{\frac{6}{x}}$$

Divide \frac{x^{2}+4}{2x} by \frac{6}{x} by multiplying \frac{x^{2}+4}{2x} by the reciprocal of \frac{6}{x}.

$$\frac{\left(x^{2}+4\right)x}{2x\times 6}$$

Cancel out x in both numerator and denominator.

$$\frac{x^{2}+4}{2\times 6}$$

Multiply 2 and 6 to get 12.

$$\frac{x^{2}+4}{12}$$

Expand

$$\frac{x^{2}}{12}+\frac{1}{3}$$

Short Solution Steps

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

$$\frac{\frac{xx}{2x}+\frac{2\times 2}{2x}}{\frac{6}{x}}$$

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

$$\frac{\frac{xx+2\times 2}{2x}}{\frac{6}{x}}$$

Do the multiplications in xx+2\times 2.

$$\frac{\frac{x^{2}+4}{2x}}{\frac{6}{x}}$$

Divide \frac{x^{2}+4}{2x} by \frac{6}{x} by multiplying \frac{x^{2}+4}{2x} by the reciprocal of \frac{6}{x}.

$$\frac{\left(x^{2}+4\right)x}{2x\times 6}$$

Cancel out x in both numerator and denominator.

$$\frac{x^{2}+4}{2\times 6}$$

Multiply 2 and 6 to get 12.

$$\frac{x^{2}+4}{12}$$