This is a limit expression you're working with. Let me transcribe and analyze it for you.

The expression in the image appears as:

$\lim_{x \to \frac{6}{5}} \frac{6 \cdot 8 \cdot x^2 - (6^2 - 8^2) \cdot x + 6 \cdot 8}{\sqrt{2 \cdot 6 \cdot x - 6^2 \cdot x + 8^2}}$

The limit is taken as $x$ approaches $\frac{6}{5}$, and the numerator and denominator involve algebraic expressions that include powers of $x$ and constants. To solve this limit, we'd likely need to simplify both the numerator and denominator to directly substitute $x = \frac{6}{5}$ or apply limit-solving techniques like factoring or L'Hopital's rule.

Would you like me to walk through the solution step by step?

Here are some related questions you might want to explore:

1. What is L'Hopital's Rule, and when can it be applied to limits like this one?
2. How do you factor complex polynomial expressions in the numerator or denominator?
3. What are other techniques for simplifying limits involving radicals or square roots?
4. How do you approach solving limits with rational functions?
5. What is the significance of the limit's result in a real-world context?

Tip: When evaluating limits, always check if you can directly substitute the value first; if you encounter indeterminate forms like 0/0, consider using algebraic manipulation or L'Hopital's Rule.