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