\(B=\frac{5}{18\cdot21}+\frac{5}{21\cdot24}+\frac{5}{24\cdot27}+...+\frac{5}{123\cdot126}\\ B=\frac{5}{3}\cdot\left(\frac{3}{18\cdot21}+\frac{3}{21\cdot24}+\frac{3}{24\cdot27}+...+\frac{3}{123\cdot126}\right)\\ B=\frac{5}{3}\cdot\left(\frac{1}{18}-\frac{1}{21}+\frac{1}{21}-\frac{1}{24}+\frac{1}{24}-\frac{1}{27}+...+\frac{1}{123}-\frac{1}{126}\right)\\ B=\frac{5}{3}\cdot\left(\frac{1}{18}-\frac{1}{126}\right)\\ B=\frac{5}{3}\cdot\left(\frac{7}{126}-\frac{1}{126}\right)\\ B=\frac{5}{3}\cdot\frac{1}{21}\\ B=\frac{5}{63}\)

Theo đề bài, ta có:

A = \(\dfrac{6}{15.18}+\dfrac{6}{18.21}+\dfrac{6}{21.24}+...+\dfrac{6}{87.90}\)

A = \(2.\left(\dfrac{3}{15.18}+\dfrac{3}{18.21}+\dfrac{3}{21.24}+...+\dfrac{3}{87.90}\right)\)

A =\(2.\left(\dfrac{1}{15}-\dfrac{1}{18}+\dfrac{1}{18}-\dfrac{1}{21}+\dfrac{1}{21}-\dfrac{1}{24}+...+\dfrac{1}{87}-\dfrac{1}{90}\right)\)

A = \(2.\left(\dfrac{1}{15}-\dfrac{1}{90}\right)\)= \(\dfrac{1}{8}\)

A= \(\dfrac{6}{15.18}+\dfrac{6}{18.21}+...+\dfrac{6}{87.90}\)

A= \(2\left(\dfrac{3}{15.18}+\dfrac{3}{18.21}+...+\dfrac{3}{87.90}\right)\)

A= \(2\left(\dfrac{1}{15}-\dfrac{1}{18}+\dfrac{1}{18}-\dfrac{1}{21}+...+\dfrac{1}{87}-\dfrac{1}{90}\right)\)

A= \(2\left(\dfrac{1}{15}-\dfrac{1}{90}\right)\)

A= 2. \(\dfrac{1}{16}\)

A= \(\dfrac{1}{8}\)

A =\(\dfrac{6}{15.18}+\dfrac{6}{18.21}+\dfrac{6}{21.24}+...+\dfrac{6}{87.90}\)

= \(\dfrac{6}{3}.\left(\dfrac{3}{15.18}+\dfrac{3}{18.21}+\dfrac{3}{21.14}+...+\dfrac{3}{87.90}\right)\)

=\(\dfrac{6}{3}.\left(\dfrac{1}{15}-\dfrac{1}{18}+\dfrac{1}{18}-\dfrac{1}{21}+\dfrac{1}{21}-\dfrac{1}{24}+...+\dfrac{1}{87}+\dfrac{1}{90}\right)\)

=\(\dfrac{6}{3}.\left(\dfrac{1}{15}-\dfrac{1}{90}\right)\)

= \(\dfrac{6}{3}.\dfrac{1}{18}=\dfrac{1}{9}\)

\(6.-\dfrac{5}{18}=-\dfrac{5}{3}\)

\(-\dfrac{13}{24}+-\dfrac{5}{21}.\dfrac{7}{25}=-\dfrac{13}{24}+-\dfrac{1}{15}=-\dfrac{73}{120}\)

\(-\dfrac{5}{13}-\dfrac{3}{26}.-\dfrac{2}{3}=-\dfrac{5}{13}-\left(-\dfrac{1}{13}\right)=-\dfrac{4}{13}\)

\(\left(\dfrac{2}{3}+-\dfrac{7}{6}\right).\left(\dfrac{3}{8}+-\dfrac{3}{24}\right)=-\dfrac{1}{2}.\dfrac{1}{4}=\dfrac{1}{8}\)

Kết quả lần lượt của các phép tính là :

\(\dfrac{-5}{3}\) , \(\dfrac{-73}{120}\) , \(\dfrac{-4}{13}\) , \(\dfrac{-1}{8}\)

a: 3/8=36/96

5/12=40/96

b: -2/9=-24/108

-5/12=-45/108

c: -3/16=-63/336

-5/24=-70/336

-21/56=-126/336

a) -3/7 + 5/13 + -4/7 = -3/7 + 4/7 + 5/13 = -1 + 5/13 = -13/13 + 5/13 = -8/13 b) -5/21 + -2/21 + 8/24 = -7/21 + 1/3 = -1/3 + 1/3 = 0

a) \(\dfrac{-3}{7}+\dfrac{5}{13}+\dfrac{-4}{7}\)

\(=\left(\dfrac{-3}{7}+\dfrac{-4}{7}\right)+\dfrac{5}{13}\)

\(=\left(-1\right)+\dfrac{5}{13}\)

\(=\dfrac{-8}{13}\)

b) \(\dfrac{-5}{21}+\dfrac{-2}{21}+\dfrac{8}{24}\)

\(=\left(\dfrac{-5}{21}+\dfrac{-2}{21}\right)+\dfrac{1}{3}\)

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

\(=0\)

Áp dụng tính chất cơ bản của phép cộng phân số:

a: \(=\dfrac{3}{8}\left(27+\dfrac{1}{5}-51-\dfrac{1}{5}\right)+19\)

\(=-24\cdot\dfrac{3}{8}+19=-9+19=10\)

b: \(=\left(35+\dfrac{1}{6}-46-\dfrac{1}{6}\right):\left(\dfrac{-4}{5}\right)\)

\(=\dfrac{-11\cdot5}{-4}=\dfrac{55}{4}\)

c: \(=\left(\dfrac{-15+8}{20}\right):\left[\dfrac{3}{7}+\dfrac{7}{3}\cdot\dfrac{12-5}{20}\right]\)

\(=\dfrac{-7}{20}:\left(\dfrac{3}{7}+\dfrac{49}{60}\right)\)

\(=-\dfrac{147}{523}\)

\(A=-B\)

\(B=\dfrac{2}{1.3}+\dfrac{2}{3.5}+...+\dfrac{2}{23.25}+\dfrac{2}{25.27}+\dfrac{1}{27}\)

\(B=\dfrac{1}{1}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+...+\dfrac{1}{23}-\dfrac{1}{25}+\dfrac{1}{25}-\dfrac{1}{27}+\dfrac{1}{27}\)

\(B=1\)

A=-1

\(A=-\dfrac{2}{1.3}-\dfrac{2}{3.5}-......-\dfrac{2}{25.27}-\dfrac{1}{27}\)

\(\Leftrightarrow A=-\left(\dfrac{2}{1.3}+\dfrac{2}{3.5}+.....+\dfrac{1}{27}\right)\)

\(\Leftrightarrow A=-\left(1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+...+\dfrac{1}{25}-\dfrac{1}{27}+\dfrac{1}{27}\right)\)

\(\Leftrightarrow A=-1\)

= -(1-1/3+1/3-1/5+1/5-1/7+..+1/19-1/21+1/21-1/23+1/23-1/25+1/25-1/27+1/27)

= -1

\(\dfrac{-3}{5}+\dfrac{28}{5}.\left(\dfrac{43}{56}+\dfrac{5}{24}-\dfrac{21}{63}\right)\)

= \(\dfrac{-3}{5}+\dfrac{28}{5}.\dfrac{9}{14}\)

= \(\dfrac{-3}{5}+\dfrac{28.9}{5.14}\)

= \(\dfrac{-3}{5}+\dfrac{18}{5}\)

= \(\dfrac{\left(-3\right)+18}{5}\)

= \(\dfrac{15}{5}=3\)

\(B=\dfrac{5}{3}x\left(\dfrac{1}{2}+\dfrac{1}{6}+\dfrac{1}{12}+\dfrac{1}{20}+...+\dfrac{1}{90}\right)=\)

\(=\dfrac{5}{3}x\left(\dfrac{1}{1x2}+\dfrac{1}{2x3}+\dfrac{1}{3x4}+\dfrac{1}{4x5}+...+\dfrac{1}{9x10}\right)\)

\(C=\dfrac{2-1}{1x2}+\dfrac{3-2}{2x3}+\dfrac{4-3}{3x4}+...+\dfrac{10-9}{9x10}=\)

\(=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{9}-\dfrac{1}{10}=\)

\(=1-\dfrac{1}{10}=\dfrac{9}{10}\)

\(\Rightarrow B=\dfrac{5}{3}xC=\dfrac{5}{3}x\dfrac{9}{10}=\dfrac{3}{2}\)