What happens to fractions?

Question

Mathematics

Hello, please tell me what is happening with the fractions in this example, as I understand it, there is a reduction, right?

Thank you in advance for your response.

Answer 1

In the first limit, just an abbreviation, yes. In the second limit, as x tends to infinity, the fractions 3/x, 5/x^2, 1/x^2, 1/x tend to zero (Because dividing a constant by an infinitely large number results in 0) . Therefore, it turns out that: (2 - 0 - 0) / (0 + 0 + 3) = 2/3