\(M=3\dfrac{1}{2022}\cdot\dfrac{1}{2024}-\dfrac{1}{506}\cdot5\dfrac{2021}{2022}-\dfrac{5}{2022\cdot2024}+\dfrac{3}{253}\)
Đặt 2022=a; 2024=b
=>\(M=3\dfrac{1}{a}\cdot\dfrac{1}{b}-\dfrac{4}{b}\left(5+1-\dfrac{1}{a}\right)-\dfrac{5}{ab}+\dfrac{3}{253}\)
\(=\dfrac{3a+1}{a}\cdot\dfrac{1}{b}-\dfrac{4}{b}\cdot\dfrac{6a-1}{a}-\dfrac{5}{ab}+\dfrac{3}{253}\)
\(=\dfrac{3a+1-24a+4-5}{ab}+\dfrac{3}{253}\)
\(=\dfrac{-21}{b}+\dfrac{3}{253}=\dfrac{-21}{2024}+\dfrac{3}{253}=\dfrac{3}{2024}\)
\(M=\left(3+\dfrac{1}{2022}\right)\cdot\dfrac{1}{2024}-\dfrac{1}{506}\cdot\left(6-\dfrac{1}{2022}\right)-\dfrac{5}{2022\cdot2024}+\dfrac{3}{253}\)
\(M=\dfrac{3}{2024}+\dfrac{1}{2022\cdot2024}-\dfrac{6}{506}+\dfrac{1}{506\cdot2022}-\dfrac{5}{2022\cdot2024}+\dfrac{3}{253}\)
\(M=\dfrac{3}{2024}+\dfrac{1}{2022\cdot2024}-\dfrac{6}{506}+\dfrac{4}{2024\cdot2022}-\dfrac{5}{2022\cdot2024}+\dfrac{6}{506}\)
\(M=\dfrac{3}{2024}\)
