\(1\frac{1}{30}:\left(24\frac{1}{6}-24\frac{1}{5}\right)-\frac{1\frac{1}{2}-\frac{3}{4}}{4x-\frac{1}{2}}=\left(-1\frac{1}{15}\right):\left(8\frac{1}{5}-8\frac{1}{3}\right)\)

\(\Rightarrow\frac{31}{30}:\left(\frac{145}{6}-\frac{121}{5}\right)-\frac{\frac{3}{2}-\frac{3}{4}}{4x-\frac{1}{2}}=\left(\frac{-16}{15}\right):\left(\frac{41}{5}-\frac{25}{3}\right)\)

\(\Rightarrow\frac{31}{30}:\left(\frac{725}{30}-\frac{726}{30}\right)-\frac{\frac{6}{4}-\frac{3}{4}}{4x-\frac{1}{2}}=\left(\frac{-16}{15}\right):\left(\frac{123}{15}-\frac{125}{15}\right)\)

\(\Rightarrow\frac{31}{30}:\frac{-1}{30}-\frac{\frac{3}{4}}{4x-\frac{1}{2}}=\frac{-16}{15}:\frac{-2}{15}\)

\(\Rightarrow\frac{31}{30}.\frac{30}{-1}-\frac{3}{4}:\left(4x-\frac{1}{2}\right)=\frac{-16}{15}.\frac{15}{-2}\)

\(\Rightarrow\left(-31\right)-\frac{3}{4}:\left(4x-\frac{1}{2}\right)=8\)

\(\Rightarrow\frac{3}{4}:\left(4x-\frac{1}{2}\right)=\left(-31\right)-8\)

\(\Rightarrow\frac{3}{4}:\left(4x-\frac{1}{2}\right)=\left(-39\right)\)

\(\Rightarrow4x-\frac{1}{2}=\frac{3}{4}:\left(-39\right)\)

\(\Rightarrow4x-\frac{1}{2}=\frac{3}{4}.\frac{-1}{39}\)

\(\Rightarrow4x-\frac{1}{2}=\frac{-1}{52}\)

\(\Rightarrow4x=\frac{-1}{52}+\frac{1}{2}\)

\(\Rightarrow4x=\frac{-1}{52}+\frac{26}{52}\)

\(\Rightarrow4x=\frac{25}{52}\)

\(\Rightarrow x=\frac{25}{52}:4\)

\(\Rightarrow x=\frac{25}{52}.\frac{1}{4}\)

\(\Rightarrow x=\frac{25}{208}\)

Vậy \(x=\frac{25}{208}\)

Chúc bn học tốt

thank you

\(=\frac{4}{3}.\frac{9}{8}.\frac{16}{15}.\frac{25}{24}...\frac{100}{99}\)

\(1\frac{1}{3}\times1\frac{1}{8}\times1\frac{1}{15}\times1\frac{1}{24}\times...\times1\frac{1}{99}\)

\(=\frac{4}{3}\times\frac{9}{8}\times\frac{16}{15}\times\frac{25}{24}\times...\times\frac{100}{99}\)

\(=\frac{2\times2}{1\times3}\times\frac{3\times3}{2\times4}\times\frac{4\times4}{3\times5}\times\frac{5\times5}{4\times6}\times...\times\frac{10\times10}{9\times11}\)

\(=\frac{2}{1}\times\frac{10}{11}\)

\(=\frac{20}{11}\)