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

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

Evaluate

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

Solution Steps

Divide \frac{1}{2}+\frac{1}{x} by \frac{1}{2} by multiplying \frac{1}{2}+\frac{1}{x} by the reciprocal of \frac{1}{2}.

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

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

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

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

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

Express \frac{x+2}{2x}\times 2 as a single fraction.

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

Cancel out 2 in both numerator and denominator.

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

Expand

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

Solution Steps

Divide \frac{1}{2}+\frac{1}{x} by \frac{1}{2} by multiplying \frac{1}{2}+\frac{1}{x} by the reciprocal of \frac{1}{2}.

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

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

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

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

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

Express \frac{x+2}{2x}\times 2 as a single fraction.

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

Cancel out 2 in both numerator and denominator.

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