Đáp án:

 $1)
a)
A=\dfrac{-337}{285}\\
b)
B=\dfrac{1}{10}\\
2)
a)
A=\dfrac{10}{3}\\
b)
B=\dfrac{71}{120}$

Giải thích các bước giải:

 $1)
a)
A=\dfrac{1}{3}-\left ( \dfrac{3}{4} \right )-\left ( \dfrac{3}{5} \right )+\dfrac{1}{57}-\dfrac{1}{36}+\dfrac{1}{15}-\dfrac{2}{9}\\
=\left (\dfrac{1}{3}-\dfrac{2}{9}  \right )\left(-\dfrac{3}{4}-\dfrac{1}{36}\right)+\left ( -\dfrac{3}{5} +\dfrac{1}{15}  \right )+\dfrac{1}{57}\\
=\left (\dfrac{3}{9}-\dfrac{2}{9}  \right )+\left(-\dfrac{27}{36}-\dfrac{1}{36}\right)+\left ( -\dfrac{9}{15} +\dfrac{1}{15}  \right )+\dfrac{1}{57}\\
=\dfrac{1}{9}-\dfrac{28}{36}-\dfrac{8}{15}+\dfrac{1}{57}\\
=\dfrac{4}{36}-\dfrac{28}{36}-\dfrac{8}{15}+\dfrac{1}{57}\\
=\dfrac{-24}{36}-\dfrac{8}{15}+\dfrac{1}{57}\\
=\dfrac{-2}{3}-\dfrac{8}{15}+\dfrac{1}{57}\\
=\dfrac{-10}{15}-\dfrac{8}{15}+\dfrac{1}{57}\\
=\dfrac{-18}{15}+\dfrac{1}{57}\\
=\dfrac{(-18).19}{285}+\dfrac{5}{285}\\
=\dfrac{-337}{285}\\
b)
B=\dfrac{1}{2}.\dfrac{1}{4}+\dfrac{1}{2}.\dfrac{1}{5}+\dfrac{1}{2}.\dfrac{1}{-4}\\
=\dfrac{1}{2}.\dfrac{1}{4}-\dfrac{1}{2}.\dfrac{1}{4}+\dfrac{1}{2}.\dfrac{1}{5}\\
=\dfrac{1}{10}\\
2)
a)
A=\dfrac{7}{1.3}+\dfrac{7}{3.5}+\dfrac{7}{5.7}+\dfrac{7}{7.9}+...+\dfrac{7}{19.21}\\
=\dfrac{7}{2}.\left ( \dfrac{2}{1.3}+\dfrac{2}{3.5}+\dfrac{2}{5.7}+\dfrac{2}{7.9}+...+\dfrac{2}{19.21} \right )\\
=\dfrac{7}{2}.\left ( 1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{9}+...+\dfrac{1}{19}-\dfrac{1}{21} \right )\\
=\dfrac{7}{2}.\left ( 1-\dfrac{1}{21} \right )\\
=\dfrac{7}{2}.\left ( \dfrac{21}{21}-\dfrac{1}{21} \right )\\
=\dfrac{7}{2}.\dfrac{20}{21}\\
=\dfrac{10}{3}\\
b)
B=\dfrac{1}{2}+\dfrac{1}{6}+\dfrac{1}{20}+\dfrac{1}{30}+\dfrac{1}{42}+\dfrac{1}{56}+\dfrac{1}{-5}\\
=\dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{4.5}+\dfrac{1}{5.6}+\dfrac{1}{6.7}+\dfrac{1}{7.8}+\dfrac{1}{-5}\\
=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{8}-\dfrac{1}{5}\\
=1-\dfrac{1}{3}+\dfrac{1}{4}-\dfrac{1}{8}-\dfrac{1}{5}\\
=\dfrac{120}{120}-\dfrac{40}{120}+\dfrac{30}{120}-\dfrac{15}{120}-\dfrac{24}{120}\\
=\dfrac{71}{120}$