Lời giải chi tiết:

 HT nhé 

1 + 3 + 2 = 6     6 - 3 -1 = 2     6 - 1 - 2 = 3

3 + 1 + 2 = 6     6 - 3 -2 = 1     6 - 1 - 3 = 2

1 + 3 + 2 =6     6 - 3 -1 =2     6 - 1 - 2 =3

3 + 1 + 2 = 6    6 - 3 -2 = 1    6 - 1 - 3 =2

5 +1 = 6     4 + 2 = 6     3 + 3 = 6

6 - 5 = 1     6 - 2 = 4     6 - 3 = 3

6 - 1 = 5     6 - 4 = 2     6 - 6 = 0

5 +1 = 6    4 + 2 = 6    3 + 3 =6

6 - 5 =1     6 - 2 =4     6 - 3 =2

6 - 1 = 5    6 - 4 = 2    6 - 6 =0

C

C

D

4 + 5 = 9     6 + 3 = 9     1 + 8 = 9

4 + 1 + 4 = 9     6 + 1 + 2 = 9     1 + 2 + 6 = 9

4 + 2 + 3 = 9     6 + 3 + 0 = 9     1 + 5 + 3 = 9

4+5 =9 .                                                  6+3=9                                                             1+8=9                         4+1+4=9                                     6+1+2=10                                             1+2+6=9                                                          4+2+3=9                     6+3+0=9                                      1+5+3=9                                                                                                                                                                                                               Đúng thì cho chứ đừng cho sai nha

Lời giải chi tiết:

\(A=\frac{1}{3}+\frac{1}{3+6}+\frac{1}{3+6+9}+...+\frac{1}{3+6+9+...+2013}\)

\(A=\frac{1}{3}.\left(1+\frac{1}{1+2}+\frac{1}{1+2+3}+...+\frac{1}{1+2+3+...671}\right)\)

\(A=\frac{1}{3}.\left(\frac{1}{\left(1+0\right).2:2}+\frac{1}{\left(1+2\right).2:2}+\frac{1}{\left(1+3\right).3:2}+...+\frac{1}{\left(1+671\right).671:2}\right)\)

\(A=\frac{1}{3}.\left(\frac{2}{1.2}+\frac{2}{2.3}+\frac{2}{3.4}+...+\frac{2}{671.672}\right)\)

\(A=\frac{1}{3}.2.\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{671.672}\right)\)

\(A=\frac{2}{3}.\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{671}-\frac{1}{672}\right)\)

\(A=\frac{2}{3}.\left(1-\frac{1}{672}\right)\)

\(A=\frac{2}{3}.\frac{671}{672}=\frac{671}{1008}\)

Bài 1: 

\(A=\dfrac{-1}{3}+1+\dfrac{1}{3}=1\)

\(B=\dfrac{2}{15}+\dfrac{5}{9}-\dfrac{6}{9}=\dfrac{2}{15}-\dfrac{1}{9}=\dfrac{18-15}{135}=\dfrac{3}{135}=\dfrac{1}{45}\)

\(C=\dfrac{-1}{5}+\dfrac{1}{4}-\dfrac{3}{4}=\dfrac{-1}{5}-\dfrac{1}{2}=\dfrac{-7}{10}\)

Bài 2: 

a: \(=\dfrac{1}{5}+\dfrac{1}{2}+\dfrac{2}{5}-\dfrac{3}{5}+\dfrac{2}{21}-\dfrac{10}{21}+\dfrac{3}{20}\)

\(=\left(\dfrac{1}{5}+\dfrac{2}{5}-\dfrac{3}{5}\right)+\left(\dfrac{2}{21}-\dfrac{10}{21}\right)+\left(\dfrac{1}{2}+\dfrac{3}{20}\right)\)

\(=\dfrac{-8}{21}+\dfrac{13}{20}=\dfrac{113}{420}\)

b: \(B=\dfrac{21}{23}-\dfrac{21}{23}+\dfrac{125}{93}-\dfrac{125}{143}=\dfrac{6250}{13299}\)

Bài 3:

\(\dfrac{7}{3}-\dfrac{1}{2}-\left(-\dfrac{3}{70}\right)=\dfrac{7}{3}-\dfrac{1}{2}+\dfrac{3}{70}=\dfrac{490}{210}-\dfrac{105}{210}+\dfrac{9}{210}=\dfrac{394}{210}=\dfrac{197}{105}\)

\(\dfrac{5}{12}-\dfrac{3}{-16}+\dfrac{3}{4}=\dfrac{5}{12}+\dfrac{3}{16}+\dfrac{3}{4}=\dfrac{20}{48}+\dfrac{9}{48}+\dfrac{36}{48}=\dfrac{65}{48}\)

Bài 4:

 \(\dfrac{3}{4}-x=1\)

\(\Rightarrow-x=1-\dfrac{3}{4}\)

\(\Rightarrow x=-\dfrac{1}{4}\)

Vậy: \(x=-\dfrac{1}{4}\)

\(x+4=\dfrac{1}{5}\)

\(\Rightarrow x=\dfrac{1}{5}-4\)

\(\Rightarrow x=-\dfrac{19}{5}\)

Vậy: \(x=-\dfrac{19}{5}\)

\(x-\dfrac{1}{5}=2\)

\(\Rightarrow x=2+\dfrac{1}{5}\)

\(\Rightarrow x=\dfrac{11}{5}\)

Vậy: \(x=\dfrac{11}{5}\)

\(x+\dfrac{5}{3}=\dfrac{1}{81}\)

\(\Rightarrow x=\dfrac{1}{81}-\dfrac{5}{3}\)

\(\Rightarrow x=-\dfrac{134}{81}\)

Vậy: \(x=-\dfrac{134}{81}\)

\(\dfrac{1}{3}+\dfrac{3}{4}+\dfrac{1}{2}=\dfrac{4}{12}+\dfrac{9}{12}+\dfrac{6}{12}=\dfrac{19}{12}\)
\(\dfrac{6}{8}+\dfrac{2}{4}+\dfrac{6}{24}=\dfrac{3}{4}+\dfrac{2}{4}+\dfrac{1}{4}=\dfrac{6}{4}=\dfrac{3}{2}\)
\(\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{5}{6}=\dfrac{3}{6}+\dfrac{2}{6}+\dfrac{5}{6}=\dfrac{10}{6}=\dfrac{5}{3}\)
\(\dfrac{3}{5}+\dfrac{3}{2}+2=\dfrac{6}{10}+\dfrac{15}{10}+\dfrac{20}{10}=\dfrac{41}{10}\)

\(\dfrac{1}{3}+\dfrac{3}{4}+\dfrac{1}{2}=\dfrac{13}{12}+\dfrac{1}{2}=\dfrac{19}{12}\\ \dfrac{6}{8}+\dfrac{2}{4}+\dfrac{6}{24}=\dfrac{5}{4}+\dfrac{6}{24}=\dfrac{3}{2}\\ \dfrac{1}{2}+\dfrac{1}{3}+\dfrac{5}{6}=\dfrac{5}{6}+\dfrac{5}{6}=\dfrac{10}{6}\\ \dfrac{3}{5}+\dfrac{3}{2}+2=\dfrac{21}{10}+\dfrac{20}{10}=\dfrac{41}{10}\)

`1/3 + 3/4 +1/2`

`= 4/12 + 9/12 + 6/12`

`= (4+9+6)/12`

`= 19/12`

__

`6/8 + 2/4 + 6/24`

`= 3/4 + 2/4 + 1/4`

`=(3+2+1)/4`

`= 6/4= 3/2`

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`1/2 + 1/3 + 5/6`

`= 3/6 + 2/6 + 5/6`

`=(3+2+5)/6`

`=10/6`

`=5/3`

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`3/5 + 3/2+2`

`= 6/10 + 15/10 + 20/10`

`=(6+15+20)/10`

`= 41/10`