\(\Leftrightarrow\left(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}\right)\times\frac{x}{3}=\frac{5}{21}\)

\(\Leftrightarrow\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}\right)\times\frac{x}{3}=\frac{5}{21}\)

\(\Leftrightarrow\left(\frac{1}{2}-\frac{1}{7}\right)\times\frac{x}{3}=\frac{5}{21}\)

\(\Leftrightarrow\frac{5}{14}\times\frac{x}{3}=\frac{5}{21}\)

\(\Leftrightarrow\frac{x}{3}=\frac{2}{3}\)

\(\Leftrightarrow x=2\)

\(\left(\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}\right).\frac{x}{3}=\frac{5}{21}\)

\(\Rightarrow\left(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}\right).\frac{x}{3}=\frac{5}{21}\)

\(\Rightarrow\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{6}-\frac{1}{7}\right).\frac{x}{3}=\frac{5}{21}\)

\(\Rightarrow\left(\frac{1}{2}-\frac{1}{7}\right).\frac{x}{3}=\frac{5}{21}\)

\(\Rightarrow\left(\frac{7}{14}-\frac{2}{14}\right).\frac{x}{3}=\frac{5}{21}\)

\(\Rightarrow\frac{5}{14}.\frac{x}{3}=\frac{5}{21}\)

\(\Rightarrow\frac{x}{3}=\frac{5}{21}:\frac{5}{14}\)

\(\Rightarrow\frac{x}{3}=\frac{2}{3}\)

\(\Rightarrow x=2\)

Vậy \(x=2\)

Đặt \(A=\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}\)

\(\Rightarrow A=\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}\)

\(\Rightarrow A=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{6}-\frac{1}{7}\)

\(\Rightarrow A=\frac{1}{2}-\frac{1}{7}=\frac{5}{14}\)

\(\Leftrightarrow\frac{5}{14}.\frac{4}{3}x=\frac{5}{14}\)

\(\Rightarrow\frac{4}{3}.x=\frac{5}{21}:\frac{5}{14}\)

\(\Rightarrow x=2\)

\(\frac{1}{3}-\left(\frac{1}{3.4}-\frac{1}{4.5}-...-\frac{1}{7.8}\right)=x-\frac{5}{18}\)

\(x-\frac{5}{18}=\frac{1}{3}-\left(\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{7}-\frac{1}{8}\right)\)

\(x-\frac{5}{18}=\frac{1}{3}-\frac{1}{3}+\frac{1}{8}\)

\(x-\frac{5}{18}=0+\frac{1}{8}\)

\(x-\frac{5}{18}=\frac{1}{8}\)

\(x=\frac{1}{8}+\frac{5}{18}\)

\(x=\frac{9}{72}+\frac{20}{72}\)

\(x=\frac{29}{72}\)

1/3 - 1/12 - 1/20 - 1/30 - 1/42 - 1/56 = x - 5/18

            1/4 - 1/20 - 1/30 - 1/42 - 1/56 = x - 5/18

                        1/5 - 1/30 - 1/42 - 1/56 = x - 5/18

                                    1/6 - 1/42 - 1/56 = x - 5/18

                                                1/7 - 1/56 = x - 5/18

                                                            1/8 = x - 5/18

                                                                x=1/8+5/18

                                                                x= 29/72

                                                           Vậy : x = 29/72

ta có:$\frac{x-1}{12}+\frac{x-1}{20}+\frac{x-1}{30}+\frac{x-1}{42}+\frac{x-1}{56}+\frac{x-1}{72}=\frac{16}{9}$

 => x+1(1/12+1/20+1/30+1/42+1/56+1/72)=16/9

=> x+1.2/9=16/9

=> x+1 = (16/9):(2/9)

=> x+1 = 8

=> x = 9

thông cảm mình ko đánh được dấu ngoặc tròn

[x-1].[1/12+1/20+1/30+1/42+1/56+1/72] =16/9

[x-1].[1/3.4+1/4.5+1/5.6+1/6.7+1/7.8+1/8.9]=16/9

[x-1].[1/3-1/9]=16/9

[x-1].2/9=16/9

x-1=16/9:2/9

x-1=8 

x=7 

Vậy x=7

Cô bé ngốc ngếch làm sai rùi. x-1 không phải x+1 nha !

 \(x+\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}=\frac{47}{42}\)

\(x+\left(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}\right)=\frac{47}{42}\)

\(x+A=\frac{47}{42}\)

     ta thấy :

              \(A=\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}\)

              \(A=\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+\frac{1}{5\cdot6}\)

                  \(A=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}\)

               \(A=\frac{1}{1}-\frac{1}{6}\)

             \(A=\frac{5}{6}\)

       vậy \(x+\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}=\frac{47}{42}\)       

  hay  \(x+\frac{5}{6}=\frac{47}{42}\)

     \(x=\frac{47}{42}-\frac{5}{6}\)

 \(x=\frac{2}{7}\)

\(x+\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}=\frac{47}{42}\)

\(x=\frac{47}{42}-\left(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}\right)\)

\(x=\frac{47}{42}-\frac{5}{6}\)

\(x=\frac{2}{7}.\)

\(\left(1-\frac{1}{2}-\frac{1}{6}-\frac{1}{12}-\frac{1}{20}-\frac{1}{30}\right)\cdot X=\frac{11}{6}\)

\(< =>\left(\frac{1}{2}-\frac{1}{12}-\frac{1}{60}\right)\cdot X=\frac{11}{6}\)

\(< =>\left(\frac{30}{60}-\frac{5}{60}-\frac{1}{60}\right)\cdot X=\frac{11}{6}\)

\(< =>\left(\frac{30-5-1}{60}\right)\cdot X=\frac{11}{6}\)

\(< =>\frac{2}{5}\cdot X=\frac{11}{6}\)

\(< =>X=\frac{11}{6}:\frac{2}{5}\)

\(< =>X=\frac{55}{12}\)

CHUC BAN HOC TOT >.<