Chữ xấu thông cảm 

\(\frac{2}{11.13}+\frac{2}{13.15}+...+\frac{2}{19.21}-x+\frac{221}{231}=\frac{4}{3}\)

\(=2\left(\frac{1}{11.13}+\frac{1}{13.15}+...+\frac{1}{19.21}\right)-x+\frac{221}{231}=\frac{4}{3}\)

\(=2.\frac{1}{2}\left(\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+...+\frac{1}{19}-\frac{1}{21}\right)-x+\frac{221}{231}=\frac{4}{3}\)

\(=\left(\frac{1}{11}-\frac{1}{21}\right)-x+\frac{221}{231}=\frac{4}{3}\)

\(=\frac{10}{231}-x+\frac{221}{231}=\frac{4}{3}\)

\(\frac{10}{231}-x=\frac{4}{3}-\frac{221}{231}\)

\(\frac{10}{231}-x=\frac{29}{77}\)

\(x=\frac{10}{231}-\frac{29}{77}\)

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

có cần cầu kì vậy ko bn, còn cách nào dễ hỉu hơn ko

\(\left(\frac{2}{11.13}+\frac{2}{13.15}+...+\frac{2}{19.21}\right)-x+4+\frac{221}{231}=\frac{7}{3}\)

\(\left(\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+...+\frac{1}{19}-\frac{1}{21}\right)-x+4=\frac{7}{3}-\frac{221}{231}\)

\(\left(\frac{1}{11}-\frac{1}{21}\right)-x+4=\frac{106}{77}\)

\(\frac{10}{231}-x=\frac{106}{77}-4\)

\(\frac{10}{231}-x=-\frac{202}{77}\)

\(x=\frac{10}{231}-\left(-\frac{202}{77}\right)\)

\(x=\frac{8}{3}\)

\(\left(\frac{2}{11.13}+\frac{2}{13.15}+...+\frac{2}{19.21}\right)-x+4+\frac{221}{231}=\frac{7}{3}\)

\(\Rightarrow\left(\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+...+\frac{1}{19}-\frac{1}{21}\right)-x+4+\frac{221}{231}=\frac{7}{3}\)

\(\frac{10}{231}-x+4+\frac{221}{231}=\frac{7}{3}\)

\(\frac{10}{231}-x+4=\frac{7}{3}-\frac{221}{231}\)

\(\frac{10}{231}-x+4=\frac{106}{77}\)

\(\frac{10}{231}-x=\frac{106}{77}-4\)

\(\frac{10}{231}-x=\frac{-202}{77}\)

\(x=\frac{10}{231}-\frac{-202}{77}\)

\(x=\frac{8}{3}\)

a.

\(\left(\frac{11}{12}+\frac{11}{12\times23}+\frac{11}{23\times34}+...+\frac{11}{89\times100}\right)+x=\frac{2}{3}\)

\(\left(\frac{11}{12}+\frac{1}{12}-\frac{1}{23}+\frac{1}{23}-\frac{1}{34}+...+\frac{1}{89}-\frac{1}{100}\right)+x=\frac{2}{3}\)

\(\left(\frac{11}{12}+\frac{1}{12}-\frac{1}{100}\right)+x=\frac{2}{3}\)

\(\left(\frac{12}{12}-\frac{1}{100}\right)+x=\frac{2}{3}\)

\(\left(1-\frac{1}{100}\right)+x=\frac{2}{3}\)

\(\left(\frac{100-1}{100}\right)+x=\frac{2}{3}\)

\(\frac{99}{100}+x=\frac{2}{3}\)

\(x=\frac{2}{3}-\frac{99}{100}\)

\(x=\frac{200-297}{300}\)

\(x=-\frac{97}{300}\)

b.

\(\left(\frac{2}{11\times13}+\frac{2}{13\times15}+...+\frac{2}{19\times21}\right)-x+\frac{221}{231}=\frac{4}{3}\)

\(\left(\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+...+\frac{1}{19}-\frac{1}{21}\right)+\frac{221}{231}-x=\frac{4}{3}\)

\(\left(\frac{1}{11}-\frac{1}{21}\right)+\frac{221}{231}-x=\frac{4}{3}\)

\(\left(\frac{21-11}{231}\right)+\frac{221}{231}-x=\frac{4}{3}\)

\(\frac{10}{231}+\frac{221}{231}-x=\frac{4}{3}\)

\(\frac{231}{231}-x=\frac{4}{3}\)

\(1-x=\frac{4}{3}\)

\(x=1-\frac{4}{3}\)

\(x=\frac{3-4}{3}\)

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

Chúc bạn học tốt

a)\(\frac{5}{7}:X=1-\frac{4}{7}=\frac{3}{7}\)

\(X=\frac{5}{7}:\frac{3}{7}=\frac{5}{3}\)

b)

\(\left(\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{14}+...+\frac{1}{19}-\frac{1}{21}\right)-X=\frac{4}{3}-\frac{221}{231}=\frac{29}{77}\)

\(\left(\frac{1}{11}-\frac{1}{21}\right)-X=\frac{29}{77}\)

\(X=\frac{10}{231}-\frac{29}{77}=-\frac{1}{3}\)

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