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The problem in the image is asking to compute a limit:

\[
\lim_{x \to \infty} \frac{\sqrt{3x^2 - 6x}}{5x - 3}
\]

Let’s go through the steps to find the limit as \(x\) approaches infinity.

### Step 1: Factor the highest power of \(x\) inside the square root
Inside the square root, the term \(3x^2 - 6x\) has \(x^2\) as the highest degree. We factor out \(x^2\) from both terms:

\[
\sqrt{3x^2 - 6x} = \sqrt{x^2(3 - \frac{6}{x})} = x\sqrt{3 - \frac{6

Compute the limit as x approaches infinity: lim(x -> ∞) [√(3x² - 6x) / (5x - 3)]

Learn how to compute the limit of √(3x² - 6x) / (5x - 3) as x approaches infinity. This problem explores asymptotic behavior, factoring techniques, and radical simplifications. Suitable for advanced high school or early college-level students.

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