\(x-\frac{20}{11\cdot13}-\frac{20}{13\cdot15}-\frac{20}{15\cdot17}-......-\frac{20}{53\cdot55}=\frac{3}{11}\)

\(\Leftrightarrow x-10\left(\frac{2}{11\cdot13}-\frac{2}{13\cdot15}-\frac{2}{15\cdot17}-.....-\frac{2}{53\cdot55}\right)=\frac{3}{11}\)

\(\Leftrightarrow x-10\left(\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+....+\frac{1}{53}-\frac{1}{55}\right)=\frac{3}{11}\)

\(\Leftrightarrow x-10\left(\frac{1}{11}-\frac{1}{55}\right)=\frac{3}{11}\)

\(\Rightarrow x=1\)

\(x-\frac{20}{11.13}-\frac{20}{13.15}-\frac{20}{15.17}-...-\frac{20}{53.55}=\frac{3}{11}\)

\(\Rightarrow x-\left(\frac{20}{11.13}+\frac{20}{13.15}+\frac{20}{15.17}+...+\frac{20}{53.55}\right)=\frac{3}{11}\)

\(\Rightarrow x-\left[10\left(\frac{2}{11.13}+\frac{2}{13.15}+\frac{2}{15.17}+...+\frac{20}{53.55}\right)\right]=\frac{3}{11}\)

\(\Rightarrow x-\left[10\left(\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+\frac{1}{15}-\frac{1}{17}+...+\frac{1}{53}-\frac{1}{55}\right)\right]=\frac{3}{11}\)

\(\Rightarrow x-\left[10\left(\frac{1}{11}-\frac{1}{55}\right)\right]=\frac{3}{11}\)

\(\Rightarrow x-\left[10.\frac{4}{55}\right]=\frac{3}{11}\)

\(\Rightarrow x-\frac{8}{11}=\frac{3}{11}\)

\(\Rightarrow x=\frac{3}{11}+\frac{8}{11}\)

\(\Rightarrow x=1\)

Vậy x = 1

_Chúc bạn học tốt_

\(x-\left(\frac{20}{11.13}+\frac{20}{13.15}+....+\frac{20}{53.55}\right)=\frac{3}{11}\)

\(x-10\left(\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+...+\frac{1}{53}-\frac{1}{55}\right)=\frac{3}{11}\)

\(x-10\left(\frac{1}{11}-\frac{1}{55}\right)=\frac{3}{11}\)

\(x-10.\frac{4}{55}=\frac{3}{11}\)

\(x-\frac{8}{11}=\frac{3}{11}\Rightarrow x=\frac{3}{11}+\frac{8}{11}=\frac{11}{11}=1\)

\(x-\left(\frac{20}{11\cdot13}+\frac{20}{13\cdot15}+...+\frac{20}{53\cdot55}\right)=\frac{3}{11}\)

Đặt \(x-A=\frac{3}{11}\)

\(\frac{A}{10}=\frac{2}{11\cdot13}+\frac{2}{13\cdot15}+...+\frac{2}{53\cdot55}\)

\(\frac{A}{10}=\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+...+\frac{1}{53}-\frac{1}{55}\)

\(\frac{A}{10}=\frac{1}{11}-\frac{1}{55}\)

\(\frac{A}{10}=\frac{4}{55}\)

\(A=\frac{8}{11}\)

\(\Rightarrow x-\frac{8}{11}=\frac{3}{11}\)

\(\Rightarrow x=\frac{3}{11}+\frac{8}{11}\)

\(\Rightarrow x=1\)

a. nhân cả hai vế của đẳng thức với 1/ 10 ta có

x/10 - (2/11.13 +2/13.15+...+2/53.55)=3/11 . 1/10

x/10 - (1/11-1/13+1/13-1/15 +...+1/53-1/55) =3/110

x/10 - (1/11 - 1/55) =3/110

x/10 -4/55 = 3/110

x/10=3/110 + 4/55

x. 1/10 =1/10

x= 1/10 : 1/10 =1

b) bạn nhân cả hai vế của đẳng thức với 1/2 rồi làm tương tự

a. nhân cả hai vế của đẳng thức với \(\frac{1}{10}\). Ta có:

\(\frac{x}{10}-\left(\frac{2}{11.13}+\frac{2}{13.15}+...\frac{2}{53.55}\right)=\frac{3}{11}.\frac{1}{10}\)

\(\frac{x}{10}-\left(\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+...\frac{1}{53}-\frac{1}{55}\right)=\frac{3}{110}\)

\(\frac{x}{10}-\left(\frac{1}{11}-\frac{1}{55}\right)=\frac{3}{110}\)

\(\frac{x}{10}-\frac{-4}{55}=\frac{3}{110}\)

\(\frac{x}{10}=\frac{3}{110}+\frac{4}{55}\)

\(x.\frac{1}{10}=\frac{1}{10}\)

\(x=\frac{1}{10}:\frac{1}{10}=1\)

b. cũng thế bạn nhân hai vế của đẳng thức với \(\frac{1}{2}\) rồi làm tương tự.

x-10( 2/11.13+2/13.15+...+2/53.55)=3/11

x-10(1/11-1/55)=3/11

x-10.4/55=3/11

x-40/55=3/11

x=3/11+40/55

x= 1

x-10.(2/11.13+2/13.15+....+2/53.55)=3/11

x-10.(1/11-1/13+...+1/53-1/55)=3/11

x-10.(1/11-1/55)=3/11

x-10.4/55=3/11

x-8/11=3/11

x=1

Nhớ k cho mình nhé

Hình như sai đề rùi bạn ạ

2x=1/11-1/13.........................-1/53-1/55+3/11

2x=1/11-1/55+3/11

2x=19/55

x=19/55 chia 2

x=19/110 

sai đề phải là cộng chứ ko phải trừ

\(x-\frac{20}{11.13}-\frac{20}{13.15}-\frac{20}{15.17}-...-\frac{20}{53.55}=\frac{3}{11}\)

\(x-10\left(\frac{2}{11.13}+\frac{2}{13.15}+\frac{2}{15.17}+...+\frac{2}{53.55}\right)=\frac{3}{11}\)

\(x-10\left(\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+\frac{1}{15}-\frac{1}{17}+...+\frac{1}{53}-\frac{1}{55}\right)=\frac{3}{11}\)

\(x-10.\frac{4}{55}=\frac{3}{11}\)

\(x=1\)