\(9\times7+8\times9-15\times9.\\ =9\times\left(7+8-15\right)=9\times0=0.\)

\(\Rightarrow\left(9\times7+8\times9-15\times9\right):\left(1+3+5+7+...+17+19\right).\\ =0:\left(1+3+5+7+...+17+19\right).\\ =0.\)

\(=\left(15\cdot9-15\cdot9\right):\left(1+3+...+17+19\right)=0\)

=9×(7+8-15)=9×0=0

=0:(1+3+5+7+...+17+19)

=0

\(E=1.2.3+2.3.4+3.4.5+...+18.19.20\)

\(4E=1.2.3.4+2.3.4.4+3.4.5.4+...+18.19.20.4\)

\(4E=1.2.3.4+2.3.4.\left(5-1\right)+3.4.5.\left(6-2\right)+...+18.19.20.\left(21-17\right)\)

\(4E=1.2.3.4+2.3.4.5-1.2.3.4+3.4.5.6-2.3.4.5+...+18.19.20.21-17.18.19.20\)

\(4E=18.19.20.21\)

\(4E=143640\)

\(E=\frac{143640}{4}\)

\(E=35910\)

Chúc bạn học tốt ~ 

\(G=2.4.6+4.6.8+6.8.10+...+18.20.22\) ( xem lại đề có nhầm dấu ko nha bn ) 

\(8G=2.4.6.8+4.6.8.8+6.8.10.8+...+18.20.22.8\)

\(8G=2.4.6.8+4.6.8.\left(10-2\right)+6.8.10.\left(12-4\right)+...+18.20.22\left(24-16\right)\)

\(8G=2.4.6.8+4.6.8.10-2.4.6.8+6.8.10.12-4.6.8.10+...+18.20.22.24-16.18.20.22\)

\(8G=18.20.22.24\)

\(8G=190080\)

\(G=\frac{190080}{8}\)

\(G=23760\)

Chúc bạn học tốt ~ 

\(H=1.3.5+3.5.7+5.7.9+...+17.19.21\)

\(8H=1.3.5.8+3.5.7.8+5.7.9.8+...+17.19.21.8\)

\(8H=1.3.5.8+3.5.7.\left(9-1\right)+5.7.9.\left(11-3\right)+...+17.19.21.\left(23-15\right)\)

\(8H=1.3.5.8+3.5.7.9-1.3.5.7+5.7.9.11-3.5.7.9+...+17.19.21.23-15.17.19.21\)

\(8H=1.3.5.8-1.3.5.7+17.19.21.23\)

\(8H=15+156009\)

\(8H=156024\)

\(H=\frac{156024}{8}\)

\(H=19503\)

Chúc bạn học tốt ~ 

giúp tui mọi người ơi

A) 5/6 + 8/21 = 153/126

B) 4/9 x 7 - 23/18 = 28/9 - 23/18 = 33/18 = 11/6

C) 3/4 : 6 + 5/16 = 3/24 + 5/16 = 7/16

bạn viết vậy khó hiểu quá bạn viết bằng kí tự phân số ik ạ

\(\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+...+\frac{1}{19\cdot20}\)

=\(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{19}-\frac{1}{20}\)(Dùng cộng rồi trừ chính số đó bằng 0)

=\(\frac{1}{2}-\frac{1}{20}\)

=\(\frac{10}{20}-\frac{1}{20}\)( Dùng phương pháp quy đồng)

=\(\frac{9}{20}\)

  Gọi S là 1.2.3+2.3.4+3.4.5+...+18.19.20

Ta có : S=1.2.3+2.3.4+3.4.5+...+18.19.20

4S=1.2.3.4+2.3.4.4+3.4.5.4+...+18.19.20.4

    =1.2.3.4+2.3.4.(5-1)+3.4.5.(6-2)+...+18.19.20.(21-17)

    =1.2.3.4+2.3.4.5-1.2.3.4+3.4.5.6-2.3.4.5+...+18.19.20.21-17.18.19.20

    =\(\frac{18.19.20.21}{4}=35910\)

1) \(\dfrac{1}{2}+\dfrac{13}{19}-\dfrac{4}{9}+\dfrac{6}{19}+\dfrac{5}{18}\)

\(=\dfrac{1}{2}+\left(\dfrac{13}{19}+\dfrac{6}{19}\right)-\dfrac{4}{9}+\dfrac{5}{18}\)

\(=\dfrac{3}{2}-\dfrac{4}{9}+\dfrac{5}{18}\)

\(=\dfrac{19}{18}+\dfrac{5}{18}\)

\(=\dfrac{24}{18}\)

\(=\dfrac{4}{3}\)

2) \(\dfrac{-20}{23}+\dfrac{2}{3}-\dfrac{3}{23}+\dfrac{2}{5}+\dfrac{7}{15}\)

\(=\left(-\dfrac{20}{23}-\dfrac{3}{23}\right)+\dfrac{2}{3}+\dfrac{2}{5}+\dfrac{7}{15}\)

\(=-1+\dfrac{2}{3}+\dfrac{2}{5}+\dfrac{7}{15}\)

\(=-\dfrac{1}{3}+\dfrac{2}{5}+\dfrac{7}{15}\)

\(=\dfrac{1}{15}+\dfrac{7}{15}\)

\(=\dfrac{8}{15}\)

3) \(\dfrac{4}{3}+\dfrac{-11}{31}+\dfrac{3}{10}-\dfrac{20}{31}-\dfrac{2}{5}\)

\(=\left(\dfrac{-11}{31}-\dfrac{20}{31}\right)+\dfrac{4}{3}+\dfrac{3}{10}-\dfrac{2}{5}\)

\(=-1+\dfrac{4}{3}+\dfrac{3}{10}-\dfrac{2}{5}\)

\(=\dfrac{1}{3}+\dfrac{3}{10}-\dfrac{2}{5}\)

\(=\dfrac{1}{3}-\dfrac{1}{10}\)

\(=\dfrac{7}{30}\)

4) \(\dfrac{5}{7}.\dfrac{5}{11}+\dfrac{5}{7}.\dfrac{2}{11}-\dfrac{5}{7}.\dfrac{14}{11}\)

\(=\dfrac{5}{7}.\left(\dfrac{5}{11}+\dfrac{2}{11}-\dfrac{14}{11}\right)\)

\(=\dfrac{5}{7}.-\dfrac{7}{11}\)

\(=-\dfrac{35}{77}\)

\(=-\dfrac{5}{11}\)

\(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{19.20}\)

\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-...+\frac{1}{19}-\frac{1}{20}\)

\(=\frac{1}{2}-\frac{1}{20}\)

\(=\frac{9}{20}\)