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M = (3+ 1/417).1/762 - 1/139(4 +761/762) - 4/417.762 + 5/139
= 3/762 + 1/417.762 - 4/139 - 761/139.762 - 4/417.762 + 5/139
= 3/762 - 3/417.762 + 1/139 - 761/139.762 =
= 1179/ 139.762 - 761/139.762 - 3/417.762 =
= 418/139.762 - 3/417.762 =418/139.762 - 1/139.762 = 417/139.762 = 3/762 = 1/254
= \(\frac{3}{762}+\frac{1}{417.762}-\frac{1}{139}.\left(4+\frac{761}{762}\right)-\frac{4}{417.762}+\frac{5}{139}\)
= \(\frac{3}{762}+\left(\frac{1}{417.762}-\frac{4}{417.762}\right)-\frac{1}{139}.\left(4+1-\frac{1}{762}\right)+\frac{5}{139}\)
= \(\frac{3}{762}+\frac{-3}{417.762}-\frac{5}{139}+\frac{1}{762.139}+\frac{5}{139}\)
= \(\frac{3}{762}+\left(\frac{-1}{139.762}+\frac{1}{762.139}\right)+\left(-\frac{5}{139}+\frac{5}{139}\right)=\frac{3}{762}=\frac{1}{254}\)
\(D=\left(3+\frac{1}{417}\right).\frac{1}{762}-\frac{1}{139}\left(4+\frac{761}{762}\right)-\frac{4}{417.762}+\frac{5}{139}\)
=\(\frac{3}{762}+\frac{1}{417.762}-\frac{4}{139}-\frac{761}{139.762}-\frac{4}{417.762}+\frac{5}{139}\)
=\(\frac{3}{762}-\frac{1}{139.762}+\frac{1}{139}-\frac{761}{139.762}=\frac{3}{762}+\frac{1}{139}\left(-\frac{1}{762}+1\right)-\frac{761}{139.762}=\)
\(\frac{3}{762}+\frac{761}{139.762}-\frac{761}{139.762}=\frac{3}{762}\)
\(M=\dfrac{1252\cdot1}{417\cdot762}-\dfrac{3\cdot3809}{417\cdot762}-\dfrac{4}{417\cdot762}+\dfrac{5}{139}\)
\(=\dfrac{-10164}{417\cdot762}=-\dfrac{1694}{52959}\)
Đặt 761=a; 139=b
\(M=\left(3+\dfrac{1}{3b}\right)\cdot\dfrac{1}{a+1}-\dfrac{1}{b}\cdot\left(4+\dfrac{a}{a+1}\right)-\dfrac{4}{\left(a+1\right)\cdot3b}+\dfrac{5}{b}\)
\(=\dfrac{9b+1}{3b}\cdot\dfrac{1}{a+1}-\dfrac{1}{b}\cdot\dfrac{4a+4}{a+1}-\dfrac{4}{3b\left(a+1\right)}+\dfrac{5}{b}\)
\(=\dfrac{9b+1-3\left(4a+4\right)-4+15\left(a+1\right)}{3b\left(a+1\right)}\)
\(=\dfrac{9b+1-12a-12-4+15a+15}{3b\left(a+1\right)}\)
\(=\dfrac{3a+9b}{3b\left(a+1\right)}=\dfrac{3\left(a+3b\right)}{3b\left(a+1\right)}=\dfrac{a+3b}{b\left(a+1\right)}\)
\(=\dfrac{761+3\cdot139}{139\left(761+1\right)}=\dfrac{589}{52959}\)
\(M\)\(=\)\(313\) \(\times\) \(\frac{4}{417}\) \(\times\) \(\frac{1}{762}\) \(-\) \(\frac{4}{417}\) \(\times\) \(\frac{1}{762}\) \(-\) \(\frac{1}{139}\) \(\times4\frac{761}{762}\)\(+\frac{1}{139}\times5\)
\(M=\)\(\frac{4}{417}\times\frac{1}{762}\times312\)\(-\frac{1}{139}\left(4\frac{761}{762}-5\right)\)
\(M=\frac{-416}{139}\times\frac{-1}{762}\)\(-\frac{1}{139}\times\frac{-1}{762}\)
\(M=\frac{-1}{762}\left(\frac{-416}{139}-\frac{1}{139}\right)\) \(=\frac{415}{105918}\)
Mình tính sai: \(M=\frac{1}{245}\)