Question

Simplify the expression$\frac{x+\frac{x}{3}}{x-\frac{x}{6}}$.

Short answer

The simplified value of expression is $\frac{8}{5}$.

Step-by-step solution

Step 1. Write down the given expression.

The given expression is$\frac{x+\frac{x}{3}}{x-\frac{x}{6}}$.

Step 2. Simplify the expression.

The given expression $\frac{x+\frac{x}{3}}{x-\frac{x}{6}}$is simplified as:

$\begin{array}{c}\frac{x+\frac{x}{3}}{x-\frac{x}{6}}=\frac{\frac{3x+x}{3}}{\frac{6x-x}{6}}\\ =\frac{\frac{4x}{3}}{\frac{5x}{6}}\\ =\frac{4x}{3}\times \frac{6}{5x}\\ =\frac{8}{5}\end{array}$

Step 3. Conclusion.

The simplified value of expression is $\frac{8}{5}$.