\(3\frac{1}{417}\times\frac{1}{762}-\frac{1}{139}\times4\frac{761}{762}-\frac{4}{417\times762}+\frac{5}{139}=?\)
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\(M=\left(\dfrac{1252}{417.762}-\dfrac{4}{417.762}\right)-\left(\dfrac{1}{139}+\dfrac{5}{139}\right).\dfrac{3809}{762}\)
\(M=\left(\dfrac{1252-4}{317754}\right)-\dfrac{6}{139}.\dfrac{3809}{762}\)
\(M=\left(\dfrac{1248}{317754}\right)-\dfrac{22854}{105918}\)
\(M=\dfrac{208}{52959}-\dfrac{3809}{17653}\)
\(M=\dfrac{3671824}{934885227}-\dfrac{201720831}{934885227}\)
\(M=\dfrac{-198049007}{934885227}\)
\(D=\left(3+\frac{1}{417}\right).\frac{1}{762}-\frac{1}{139}\left(4+\frac{761}{762}\right)-\frac{4}{417.762}+\frac{5}{139}\)
=\(\frac{3}{762}+\frac{1}{417.762}-\frac{4}{139}-\frac{761}{139.762}-\frac{4}{417.762}+\frac{5}{139}\)
=\(\frac{3}{762}-\frac{1}{139.762}+\frac{1}{139}-\frac{761}{139.762}=\frac{3}{762}+\frac{1}{139}\left(-\frac{1}{762}+1\right)-\frac{761}{139.762}=\)
\(\frac{3}{762}+\frac{761}{139.762}-\frac{761}{139.762}=\frac{3}{762}\)
\(M\)\(=\)\(313\) \(\times\) \(\frac{4}{417}\) \(\times\) \(\frac{1}{762}\) \(-\) \(\frac{4}{417}\) \(\times\) \(\frac{1}{762}\) \(-\) \(\frac{1}{139}\) \(\times4\frac{761}{762}\)\(+\frac{1}{139}\times5\)
\(M=\)\(\frac{4}{417}\times\frac{1}{762}\times312\)\(-\frac{1}{139}\left(4\frac{761}{762}-5\right)\)
\(M=\frac{-416}{139}\times\frac{-1}{762}\)\(-\frac{1}{139}\times\frac{-1}{762}\)
\(M=\frac{-1}{762}\left(\frac{-416}{139}-\frac{1}{139}\right)\) \(=\frac{415}{105918}\)
\(M=\dfrac{1252\cdot1}{417\cdot762}-\dfrac{3\cdot3809}{417\cdot762}-\dfrac{4}{417\cdot762}+\dfrac{5}{139}\)
\(=\dfrac{-10164}{417\cdot762}=-\dfrac{1694}{52959}\)
= \(\frac{3}{762}+\frac{1}{417.762}-\frac{1}{139}.\left(4+\frac{761}{762}\right)-\frac{4}{417.762}+\frac{5}{139}\)
= \(\frac{3}{762}+\left(\frac{1}{417.762}-\frac{4}{417.762}\right)-\frac{1}{139}.\left(4+1-\frac{1}{762}\right)+\frac{5}{139}\)
= \(\frac{3}{762}+\frac{-3}{417.762}-\frac{5}{139}+\frac{1}{762.139}+\frac{5}{139}\)
= \(\frac{3}{762}+\left(\frac{-1}{139.762}+\frac{1}{762.139}\right)+\left(-\frac{5}{139}+\frac{5}{139}\right)=\frac{3}{762}=\frac{1}{254}\)