https://r2.erweima.ai/mathbot/image/1724276800516i5qg2c7x.jpg

The image you provided shows an expression that likely involves limits in calculus. However, the notation is a bit unclear due to the quality of the image, but I will do my best to interpret and solve it.

The expression appears to be a quotient involving a limit:

\[
\frac{(x+1)(x+1) - 3}{2 + 1(x)}
\]

If the expression is intended to find the derivative using the definition of a limit, it could resemble the form of a difference quotient:

\[
\lim_{h \to 0} \frac{f(x+h) - f(x)}{h}
\]

However, the exact problem is not clear. Here’s how I would approach solving the problem, based on what I can interpret:

1. **Simplify the Expression**: Simplify both the numerator and the denominator.
2. **Apply Limits**: If it is indeed a limit problem, I would substitute the limit (as \( h \) approaches 0 or some other value).
3. **Differentiate if Necessary**: If the goal is to find the derivative, we will apply the rules of differentiation.

### Steps to Simplify and Analyze:

1. **Simplify the numerator**: \( (x+1)(x+1) - 3 \) could be expanded.
2. **Simplify the denominator**: \( 2 + 1(x) \) simplifies to \( 2 + x \).
3. **Combine and Simplify**: Combine the simplified numerator and denominator.
4. **Evaluate the limit**: If this is a limit problem, evaluate the limit.

Please confirm if this is indeed a problem involving limits or differentiation, or if there's any specific aspect you would like to focus on. If there are additional details, please share them.

Would you like a detailed step-by-step solution based on this interpretation? 

Here are five related questions:

1. What is the correct interpretation of the problem statement?
2. Are there any special conditions or additional terms in the problem that were not clear from the image?
3. Would you like to focus on the limit definition of a derivative or just simplifying the expression?
4. Do you need help with expanding and simplifying algebraic expressions?
5. How do you typically approach problems involving limits?

**Tip:** When working with limits, always check if you can simplify the expression first before applying the limit to avoid indeterminate forms like \( \frac{0}{0} \).

Explore how to simplify and analyze mathematical expressions involving derivatives and limits. This problem involves interpreting and solving expressions with limits and differentiation. Learn step-by-step methods to simplify algebraic expressions and apply limits effectively.

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