Evaluate: /(4+\frac{){2} x} /(x) 3+/(1) 6

Expression: $$\frac { 4 + \frac { 2 } { x } } { \frac { x } { 3 } + \frac { 1 } { 6 } }$$

To add or subtract expressions, expand them to make their denominators the same. Multiply $4$ times $\frac{x}{x}$.

$$\frac{\frac{4x}{x}+\frac{2}{x}}{\frac{x}{3}+\frac{1}{6}}$$

Since $\frac{4x}{x}$ and $\frac{2}{x}$ have the same denominator, add them by adding their numerators.

$$\frac{\frac{4x+2}{x}}{\frac{x}{3}+\frac{1}{6}}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of $3$ and $6$ is $6$. Multiply $\frac{x}{3}$ times $\frac{2}{2}$.

$$\frac{\frac{4x+2}{x}}{\frac{2x}{6}+\frac{1}{6}}$$

Since $\frac{2x}{6}$ and $\frac{1}{6}$ have the same denominator, add them by adding their numerators.

$$\frac{\frac{4x+2}{x}}{\frac{2x+1}{6}}$$

Divide $\frac{4x+2}{x}$ by $\frac{2x+1}{6}$ by multiplying $\frac{4x+2}{x}$ by the reciprocal of $\frac{2x+1}{6}$.

$$\frac{\left(4x+2\right)\times 6}{x\left(2x+1\right)}$$

Factor the expressions that are not already factored.

$$\frac{2\times 6\left(2x+1\right)}{x\left(2x+1\right)}$$

Cancel out $2x+1$ in both numerator and denominator.

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

Expand the expression.

$$\frac{12}{x}$$