The problem asks us to evaluate the expression $A = \frac{2023 \times 2025 + 1}{2024}$.

1. Problem Description

The problem asks us to evaluate the expression $A = \frac{2023 \times 2025 + 1}{2024}$.

2. Solution Steps

Let $x = 2024$. Then, we can rewrite the expression as

$A = \frac{(x-1)(x+1) + 1}{x}$.

We can expand the numerator:

$(x-1)(x+1) + 1 = x^2 - 1 + 1 = x^2$.

Therefore,

$A = \frac{x^2}{x} = x$.

Substituting $x = 2024$ back into the expression, we get $A = 2024$.

3. Final Answer

2024