Bonjour,
[tex]A = \frac{2}{3} - \frac{\frac{7}{3}*8}{21} = \frac{2}{3} - \frac{\frac{8}{3}*7}{3*7}= \frac{2}{3} - \frac{\frac{8}{3}}{3}= \frac{2}{3} - \frac{8}{3*3}\\ \\A= \frac{2}{3} - \frac{8}{9}= \frac{2}{3} - \frac{8}{9}= \frac{2*3}{3*3} - \frac{8}{9}= \frac{6}{9} - \frac{8}{9}= \frac{6 - 8}{9}\\\\\boxed{A= -\frac{2}{9}}[/tex]
[tex]B = \frac{\left(\frac{3}{4} - \frac{5}{6}\right)*3}{2} = \frac{\left(\frac{3*3}{4*3} - \frac{5*2}{6*2}\right)*3}{2} = \frac{\left(\frac{9}{12} - \frac{10}{12}\right)*3}{2} = \frac{\left(\frac{9-10}{12}\right)*3}{2} \\\\B = \frac{-\frac{1}{12}*3}{2} = \frac{-\frac{3}{12}}{2} = -\frac{3}{12*2} = -\frac{3}{3*4*2}\\ \\\boxed{B = -\frac{1}{8}}[/tex]
[tex]C = \frac{\left(\frac{24}{15}+\frac{35}{25}\right)*20}{33} = \frac{\left(\frac{8*3}{5*3}+\frac{7*5}{5*5}\right)*20}{33} = \frac{\left(\frac{8}{5}+\frac{7}{5}\right)*20}{33} = \frac{\left(\frac{8+7}{5}\right)*20}{33}\\\\C = \frac{\frac{15}{5}*20}{33} = \frac{\frac{5*3}{5}*20}{33} = \frac{3*20}{33} = \frac{3*20}{3*11} \\\\\boxed{C = \frac{20}{11}}[/tex]
[tex]D = \frac{\frac{5}{6}-\frac{5}{4}}{\frac{1}{2}+\frac{2}{3}} = \frac{\frac{5*2}{6*2}-\frac{5*3}{4*3}}{\frac{1*3}{2*3}+\frac{2*2}{3*2}} = \frac{\frac{10}{12}-\frac{15}{12}}{\frac{3}{6}+\frac{4}{6}} = \frac{\frac{10-15}{12}}{\frac{3+4}{6}} \\\\D = \frac{-\frac{5}{12}}{\frac{7}{6}} = -\frac{5}{12}*\frac{6}{7} = -\frac{5*6}{2*6*7}\\\\\boxed{D = -\frac{5}{14}}[/tex]
Bonne journée,
Thomas
