\(=7-\dfrac{4}{3}+\dfrac{1}{3}-6-\dfrac{5}{4}+\dfrac{4}{3}-5+\dfrac{7}{4}-\dfrac{5}{3}\)

\(=\left(7-6-5\right)-\left(\dfrac{4}{3}-\dfrac{4}{3}+\dfrac{5}{3}-\dfrac{1}{3}\right)-\left(\dfrac{5}{4}-\dfrac{7}{4}\right)\)

\(=-4-\dfrac{4}{3}-\left(\dfrac{-1}{2}\right)\)

\(=-4-\dfrac{4}{3}+\dfrac{1}{2}\)

\(=-\dfrac{24}{6}-\dfrac{8}{6}+\dfrac{3}{6}\)

\(=-\dfrac{32}{6}+\dfrac{3}{6}\)

\(=-\dfrac{29}{6}\)

\(\dfrac{1}{12}\). \(\dfrac{37}{39}+\dfrac{1}{12}.\dfrac{2}{39}+\dfrac{1}{4}\)

=\(\dfrac{1}{12}.\left(\dfrac{37}{39}+\dfrac{2}{39}\right)+\dfrac{1}{4}\)

=\(\dfrac{1}{12}.1+\dfrac{1}{4}\)

=\(\dfrac{13}{12}+\dfrac{1}{4}\)

=\(\dfrac{16}{12}\)

\(=\left(\dfrac{4}{12}-\dfrac{3}{12}\right)^2+\left(\dfrac{3}{6}-\dfrac{1}{6}\right)^2+\dfrac{4}{3}\)

\(=\dfrac{1}{144}+\dfrac{1}{9}+\dfrac{4}{3}=\dfrac{209}{144}\)

1: \(=\dfrac{16}{15}\left(-\dfrac{4}{9}+\dfrac{3}{7}\right)+\dfrac{16}{15}\left(\dfrac{4}{7}-\dfrac{5}{9}\right)\)

\(=\dfrac{16}{15}\left(-\dfrac{4}{9}+\dfrac{3}{7}+\dfrac{4}{7}-\dfrac{5}{9}\right)=0\)

2: \(=\dfrac{29}{9}\left(15+\dfrac{4}{7}-8-\dfrac{1}{7}+\dfrac{15}{7}-\dfrac{1}{7}\right)\)

\(=\dfrac{20}{9}\cdot\left(7\cdot\dfrac{18}{7}\right)=\dfrac{20}{9}\cdot18=40\)

2)

\(2+\dfrac{5}{7}+\left(\dfrac{\dfrac{3}{19}+\dfrac{3}{23}-\dfrac{3}{28}}{\dfrac{5}{19}+\dfrac{5}{23}-\dfrac{5}{28}}\right)\cdot x=\dfrac{20}{7}\\ \left[\dfrac{3\cdot\left(\dfrac{1}{19}+\dfrac{1}{23}-\dfrac{1}{28}\right)}{5\cdot\left(\dfrac{1}{19}+\dfrac{1}{23}-\dfrac{1}{28}\right)}\right]\cdot x=\dfrac{20}{7}-\dfrac{5}{7}-2\\ \dfrac{3}{5}x=\dfrac{15}{7}-2\\ \dfrac{3}{5}x=\dfrac{1}{7}\\ x=\dfrac{5}{21}\)

\(\dfrac{\dfrac{2}{5}+\dfrac{2}{7}-\dfrac{2}{11}}{\dfrac{3}{5}+\dfrac{3}{7}-\dfrac{3}{11}}+\dfrac{\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{7}}{\dfrac{3}{4}-\dfrac{3}{5}+\dfrac{3}{7}}=\dfrac{2\left(\dfrac{1}{5}+\dfrac{1}{7}-\dfrac{1}{11}\right)}{3\left(\dfrac{1}{5}+\dfrac{1}{7}-\dfrac{1}{11}\right)}+\dfrac{\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{7}}{3\left(\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{7}\right)}\)

\(=\dfrac{2}{3}+\dfrac{1}{3}\)

\(=1\)

\(=\dfrac{\dfrac{1}{3}-\dfrac{1}{7}-\dfrac{1}{13}}{2.\left(\dfrac{1}{3}-\dfrac{1}{7}-\dfrac{1}{13}\right)}.\dfrac{3.\left(\dfrac{1}{4}-\dfrac{1}{16}-\dfrac{1}{64}-\dfrac{1}{264}\right)}{\dfrac{1}{4}-\dfrac{1}{16}-\dfrac{1}{64}-\dfrac{1}{264}}\)

\(=\dfrac{1}{2}.3=\dfrac{3}{2}\)

Edogawa Conan !hình như là thiếu

bài này có trong sách Nâng cao và Phát triển bạn nhé

\(B=\dfrac{3}{2}\times\dfrac{4}{3}\times\dfrac{5}{4}\times...\times\dfrac{100}{99}\)

\(B=\dfrac{3.4.5.....100}{2.3.4.....99}\)

\(B=\dfrac{100}{2}\)

\(B=50\)