Tính tổng: $M$ = $3$$\frac{1}{417}$ . $\frac{1}{762}$ – $\frac{1}{139}$ . $4$$\frac{761}{762}$ – $\frac{4}{417.762}$ + $\frac{5}{139}$

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1. Giải thích các bước giải:

   Ta có:

   $M=3\dfrac{1}{417}\cdot\dfrac1{762}-\dfrac1{139}\cdot 4\dfrac{761}{762}-\dfrac4{417\cdot 762}+\dfrac5{139}$

   $\to M=(3+\dfrac{1}{417})\cdot\dfrac1{762}-\dfrac1{139}\cdot( 4+\dfrac{761}{762})-\dfrac4{417\cdot 762}+\dfrac5{139}$

   $\to M=(3+\dfrac{1}{417})\cdot\dfrac1{762}-\dfrac1{139}\cdot( 4+1-\dfrac{1}{762})-\dfrac4{417\cdot 762}+\dfrac5{139}$

   $\to M=(3+\dfrac{1}{417})\cdot\dfrac1{762}-\dfrac1{139}\cdot( 5-\dfrac{1}{762})-\dfrac4{417\cdot 762}+\dfrac5{139}$

   $\to M=(3\cdot\dfrac1{762}+\dfrac{1}{417}\cdot\dfrac1{762})-(\dfrac1{139}\cdot 5-\dfrac1{139}\cdot\dfrac{1}{762})-\dfrac4{417\cdot 762}+\dfrac5{139}$

   $\to M=3\cdot\dfrac1{762}+\dfrac{1}{417}\cdot\dfrac1{762}-\dfrac5{139}+\dfrac1{139}\cdot\dfrac{1}{762}-\dfrac4{417\cdot 762}+\dfrac5{139}$

   $\to M=(\dfrac5{139}-\dfrac5{139})+(\dfrac1{417\cdot 762}-\dfrac4{417\cdot 762})+(3\cdot \dfrac1{762}+\dfrac1{139}\cdot\dfrac1{762})$

   $\to M=0+(-\dfrac3{417\cdot 762})+\dfrac1{762}(3+\dfrac1{139})$

   $\to M=-\dfrac3{417\cdot 762}+\dfrac1{762}(3+\dfrac1{139})$

   $\to M=\dfrac1{762}\cdot (-\dfrac1{139}+3+\dfrac1{139})$

   $\to M=\dfrac1{762}\cdot 3$

   $\to M=\dfrac1{254}$

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