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 !

2 2/9 - x = 1/12 + 1/20 + 1/30 + 1/42 + 1/56 + 1/72

20/9 - x = 1/3×4 + 1/4×5 + 1/5×6 + 1/6×7 + 1/7×8 + 1/8×9

20/9 - x = 1/3 - 1/4 + 1/4 - 1/5 + ... + 1/8 - 1/9

20/9 - x = 1/3 - 1/9

20/9 - x = 3/9 - 1/9

20/9 - x = 2/9

x = 20/9 - 2/9

x = 18/9 = 2

Vậy x = 2

Nhớ tick và theo dõi mik nhá!

A = \(\frac{-79}{90}\)

B = \(\frac{8}{9}\)

cách giải sao chỉ mình với

\(\frac{20}{9}-x=\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{8.9}=\frac{1}{3}-\frac{1}{4}+...+\frac{1}{8}-\frac{1}{9}=\frac{1}{3}-\frac{1}{9}=\frac{2}{9}\)

\(\Rightarrow\frac{20}{9}-x=\frac{2}{9}\Rightarrow x=\frac{20}{9}-\frac{2}{9}=\frac{18}{9}=2\)

Vậy x = 2.

k cho mk nha

\(2\frac{2}{9}-x=\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}\)

\(2\frac{2}{9}-x=\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+\frac{1}{5\cdot6}+\frac{1}{6\cdot7}+\frac{1}{7\cdot8}+\frac{1}{8\cdot9}\)

\(2\frac{2}{9}-x=\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}\)

\(2\frac{2}{9}-x=\frac{1}{3}-\frac{1}{9}\)

\(2\frac{2}{9}-x=\frac{3}{9}-\frac{1}{9}\)

\(2\frac{2}{9}-x=\frac{2}{9}\)

\(x=2\frac{2}{9}-\frac{2}{9}\)

\(x=2\)

Vậy x = 2

\(2\frac{2}{9}-x=\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}\)

\(2\frac{2}{9}-x=\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}+\frac{1}{8.9}\)

\(2\frac{2}{9}-x=\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}\)

\(2\frac{2}{9}-x=\frac{1}{3}-\frac{1}{9}\)

\(2\frac{2}{9}-x=\frac{2}{9}\)

\(x=2\frac{2}{9}-\frac{2}{9}\)

\(x=2\)

Vậy x = 2

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

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

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

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

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

\(\Leftrightarrow x=2\)

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

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

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

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

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

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

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

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

\(\Rightarrow x=2\)

Vậy \(x=2\)

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

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

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

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

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

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

\(\Rightarrow x=2\)

1/1.2+1/2.3+1/3.4+1/4.5+1/5.6+1/6.7+1/7.8+1/8.9

=1-1/2+1/2-1/3+1/3-1/4+...+1/8-1/9

=1-1/9

=8/9

A) \(x = {7 \over 10}- {8 \over10} \)

\(x = {-1 \over 10}\)

B)\({2 \over3}x = 2{5 \over 6}-{3 \over4}\)

\({2 \over3}x = {25 \over 12}\)

\(x = {25 \over 12}/{2 \over3} \)

\(x = {25\over 8}\)

2/ Tính tổng:

\( = {8 \over 9}\)

\(\Leftrightarrow\)\(\frac{1}{3}\)-\(\frac{1}{3}\)+\(\frac{1}{4}\)-\(\frac{1}{4}\)+\(\frac{1}{5}\)-....+\(\frac{1}{10}\)=x-\(\frac{113}{260}\)

\(\Leftrightarrow\)x-\(\frac{113}{260}\)=\(\frac{1}{10}\)

\(\Leftrightarrow\)x=\(\frac{139}{260}\)