\(A=\dfrac{\dfrac{1}{2}+\dfrac{1}{3}+...+\dfrac{1}{2023}}{\dfrac{2022}{1}+\dfrac{2021}{2}+...+\dfrac{1}{2022}}\)
\(=\dfrac{\dfrac{1}{2}+\dfrac{1}{3}+...+\dfrac{1}{2023}}{\left(1+\dfrac{2021}{2}\right)+\left(1+\dfrac{2020}{3}\right)+...+\left(\dfrac{1}{2022}+1\right)+1}\)
\(=\dfrac{\dfrac{1}{2}+\dfrac{1}{3}+...+\dfrac{1}{2023}}{\dfrac{2023}{2}+\dfrac{2023}{3}+...+\dfrac{2023}{2022}+\dfrac{2023}{2023}}\)
\(=\dfrac{\dfrac{1}{2}+\dfrac{1}{3}+...+\dfrac{1}{2023}}{2023\left(\dfrac{1}{2}+\dfrac{1}{3}+...+\dfrac{1}{2022}+\dfrac{1}{2023}\right)}=\dfrac{1}{2023}\)
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