https://file.aiquickdraw.com/mathbot/file/1726545215860u9sz875d.jpg

The expression from the image is:

\[
\frac{x^3 - 2x^2 + x - 1}{x - 1} + \sqrt{4x^2 - 12x + 9}
\]

Let me help you simplify and solve it step by step:

### Step 1: Simplify the rational expression.
The first term is \(\frac{x^3 - 2x^2 + x - 1}{x - 1}\). This can be simplified by performing polynomial division.

### Step 2: Simplify the square root.
The second term is \(\sqrt{4x^2 - 12x + 9}\), which can potentially be factored before simplifying the square root.

Let me calculate these steps.It seems like I can’t do more advanced data analysis right now. Please try again later.

Would you like me to guide you step by step on how to solve this manually or provide any additional clarifications? Here are some related questions you could explore:

1. How do you perform polynomial division to simplify the rational expression?
2. How can you factor quadratic expressions under a square root?
3. What is the general method for simplifying square root expressions involving quadratic equations?
4. What happens when there are common factors in the numerator and denominator of a rational expression?
5. How can you check your work when simplifying complex algebraic expressions?

**Tip:** Always start by checking if terms can be factored before applying other operations like division or square roots!

Simplify and solve the expression: (x^3 - 2x^2 + x - 1) / (x - 1) + √(4x^2 - 12x + 9)

Learn how to simplify and solve a complex algebraic expression involving polynomial division and square roots. This problem includes key concepts such as polynomial division, factoring, and simplifying square root expressions. Suitable for students in Grades 10-12.

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