The image shows a mathematical expression. I'll write down and analyze it as best as I can from the image:

The expression is: $\left( \frac{1}{3} - \frac{1}{2} \right) \div \frac{1}{4} + 1$

Let's break down the solution step-by-step.

Step 1: Simplify the Parentheses

First, calculate $\frac{1}{3} - \frac{1}{2}$.

$\frac{1}{3} - \frac{1}{2} = \frac{2 - 3}{6} = -\frac{1}{6}$

Step 2: Division by a Fraction

Now we have: $-\frac{1}{6} \div \frac{1}{4}$

Dividing by a fraction is the same as multiplying by its reciprocal: $-\frac{1}{6} \times 4 = -\frac{4}{6} = -\frac{2}{3}$

Step 3: Adding 1

Now add 1 to $-\frac{2}{3}$: $-\frac{2}{3} + 1 = \frac{-2 + 3}{3} = \frac{1}{3}$

Final Answer

$\frac{1}{3}$

Would you like further details on this solution, or do you have any additional questions?

Here are some related questions that might help expand understanding:

1. How do you handle division of fractions?
2. What is the process for finding a common denominator?
3. Can we simplify complex fractions differently?
4. How would the result change if a different operation were used instead of addition at the end?
5. How do parentheses affect the order of operations?

Tip: Always handle operations inside parentheses first to simplify complex expressions efficiently.