https://file.aiquickdraw.com/mathbot/file/1726424291934c5e897m8.jpg

The cancellation in the expression shown in the image is **incorrect**. Let's analyze why.

The expression under consideration is:
\[
\frac{\frac{1}{2}}{\frac{2}{2} + \frac{\sqrt{3}}{2}}
\]

The cancellation happens in the denominator, where \( \frac{2}{2} \) and \( \frac{\sqrt{3}}{2} \) appear. However, cancellation can only be performed if there is a common factor in both terms of the entire denominator.

### Denominator analysis:
The denominator is:
\[
\frac{2}{2} + \frac{\sqrt{3}}{2} = 1 + \frac{\sqrt{3}}{2}
\]
This is a sum, not a product. Therefore, we cannot cancel out any factors between these terms.

### Correct approach:
1. The denominator should be simplified first by combining the fractions:
   \[
   \frac{1 + \sqrt{3}}{2}
   \]
2. The entire expression becomes:
   \[
   \frac{\frac{1}{2}}{\frac{1 + \sqrt{3}}{2}} = \frac{1}{1 + \sqrt{3}}
   \]
3. This is now a single fraction, and no cancellation is possible as attempted in the image.

Would you like to proceed with rationalizing this denominator, or do you have further questions?

---

### Follow-up Questions:
1. How do you rationalize a denominator like \( \frac{1}{1 + \sqrt{3}} \)?
2. What is the process for simplifying complex fractions?
3. Why can't cancellation happen in sums of terms?
4. Can you solve for simpler fractions before working on mixed terms involving square roots?
5. How do you handle square roots when they appear in fractions?

### Tip:
When simplifying expressions, cancellation can only happen when the entire numerator and denominator share a common factor, not just parts of the expression.

Explore the correct method for simplifying a complex fraction involving square roots and why cancellation is not allowed in sums. This problem focuses on algebraic principles and fraction simplification rules, suitable for students in Grades 9-11.

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