x = 0 ???

Đây là toán lớp 4?!

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\(\sqrt{\frac{1}{2}}\times\sqrt{\frac{6}{2}}\)

\(=\sqrt{\frac{1}{2}\times\frac{6}{2}}\)

\(=\sqrt{\frac{6}{4}}\)

\(=\sqrt{\frac{3}{2}}\)

\(\left(1-\frac{1}{3}\right)\times\left(1-\frac{1}{4}\right)\times\left(1-\frac{1}{5}\right)\times\left(1-\frac{1}{6}\right)\times\left(1-\frac{1}{7}\right)\times\left(1-\frac{1}{8}\right)-\frac{1}{4}\times\frac{1}{2}\)

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

\(=\frac{2}{8}-\frac{1}{4}\times\frac{1}{2}\)

\(=\frac{2}{8}-\frac{1}{8}=\frac{1}{8}\)

\(\frac{13}{24}\times\frac{12}{13}\)

\(=\frac{12}{24}=\frac{1}{2}\)

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\(\frac{1}{2}:\frac{3}{2}:\frac{5}{4}:\frac{6}{5}:\frac{7}{6}:\frac{8}{7}\)

\(=\frac{1}{2}\cdot\frac{2}{3}\cdot\frac{4}{5}\cdot\frac{5}{6}\cdot\frac{6}{7}\cdot\frac{7}{8}\)

\(=\frac{1\cdot\left(2\cdot5\cdot6\cdot7\right)}{8\cdot3\cdot\left(2\cdot5\cdot6\cdot7\right)}\)

\(=\frac{1}{24}\)

\(\frac{1}{2}\cdot\frac{2}{3}\cdot\frac{3}{4}\cdot\frac{4}{5}\cdot\frac{5}{6}\cdot\frac{6}{7}\cdot\frac{7}{8}\cdot\frac{8}{9}\cdot\frac{9}{10}\)

\(=\frac{1\cdot\left(2\cdot3\cdot4\cdot5\cdot6\cdot7\cdot8\cdot9\right)}{\left(2\cdot3\cdot4\cdot5\cdot6\cdot7\cdot8\cdot9\right)\cdot10}\)

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

\(a.\frac{4}{3}-\frac{3}{2}:X=\frac{1}{6}\)

           \(\frac{3}{2}:X=\frac{4}{3}-\frac{1}{6}\)

           \(\frac{3}{2}:X=\frac{8}{6}-\frac{1}{6}\)

           \(\frac{3}{2}:X=\frac{7}{6}\)

               \(X=\frac{3}{2}:\frac{7}{6}\)

              \(X=\frac{3}{2}\times\frac{6}{7}\)

              \(X=\frac{9}{7}\)

\(b.\left(X+\frac{2}{3}\right):\frac{1}{3}=\frac{41}{3}\)

    \(X-\frac{2}{3}=\frac{41}{3}.\frac{1}{3}\)

   \(X-\frac{2}{3}=\frac{41}{9}\)

  \(X=\frac{41}{9}+\frac{2}{3}\)

  \(X=\frac{41}{9}+\frac{6}{9}\)

 \(X=\frac{47}{9}\)

\(\left(1-\frac{2}{5}\right)\times\left(1-\frac{2}{7}\right)\times\left(1-\frac{2}{9}\right)\times\left(1-\frac{2}{11}\right)\times\left(1-\frac{2}{13}\right)\)

\(=\frac{3}{5}\times\frac{5}{7}\times\frac{7}{9}\times\frac{9}{11}\times\frac{11}{13}=\frac{3}{13}\)