Question

In the following exercises, simplify.

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

Short answer

The simplified form of the given expression is $\frac{4}{17}$.

Step-by-step solution

Step 1. Given information.

The given expression is:

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

Step 2. Concept.

The following concept is required for simplification:

$\frac{A}{B}÷\frac{C}{D}=\frac{A}{B}·\frac{D}{C}$

Step 3. Rewrite the expression and then simplify.

Simplify the numerator and denominator.

$$\begin{gathered} =\frac{\frac{3-1}{6}}{\frac{8+9}{12}} \\ =\frac{\frac{2}{6}}{\frac{17}{12}} \\ =\frac{\frac{1}{3}}{\frac{17}{12}} \end{gathered}$$

Rewrite as the product of first times the reciprocal of the second.

$$\begin{gathered} =\frac{1}{3}·\frac{12}{17} \\ =\frac{4}{17} \end{gathered}$$

Step 4. Conclusion.

The simplified form of the given expression is $\frac{4}{17}$.