Đáp án:
$a)
\dfrac{55}{117}\\
b)
\dfrac{1}{2005}\\
c)
0$
Giải thích các bước giải:
$a)
\left [ \dfrac{5}{3}\left ( -\dfrac{3}{5}+\dfrac{8}{13}-\dfrac{4}{10} \right ) \right ]:\dfrac{-15}{11}\\
=\left [ \dfrac{5}{3}\left ( -\dfrac{3}{5}+\dfrac{8}{13}-\dfrac{2}{5} \right ) \right ].\dfrac{-11}{15}\\
=\left [ \dfrac{5}{3}\left ( -\dfrac{5}{5}+\dfrac{8}{13} \right ) \right ].\dfrac{-11}{15}\\
=\left [ \dfrac{5}{3}\left ( -\dfrac{13}{13}+\dfrac{8}{13} \right ) \right ].\dfrac{-11}{15}\\
=\left [ \dfrac{5}{3}.\dfrac{-5}{13} \right ].\dfrac{-11}{15}\\
=\dfrac{-25}{39}.\dfrac{-11}{15}\\
=\dfrac{55}{117}\\
b)
\left ( 1-\dfrac{1}{2} \right ).\left ( 1-\dfrac{1}{3} \right )....\left ( 1-\dfrac{1}{2005} \right )\\
=\dfrac{1}{2}.\dfrac{2}{3}....\dfrac{2004}{2005}\\
=\dfrac{1}{2005}\\
c)
\left ( \dfrac{1}{99}+\dfrac{12}{949}+\dfrac{123}{9499} \right ).\left ( \dfrac{1}{2}-\dfrac{1}{3}-\dfrac{1}{6} \right )\\
=\left ( \dfrac{1}{99}+\dfrac{12}{949}+\dfrac{123}{9499} \right ).\left ( \dfrac{3}{6}-\dfrac{2}{6}-\dfrac{1}{6} \right )\\
=\left ( \dfrac{1}{99}+\dfrac{12}{949}+\dfrac{123}{9499} \right ). \dfrac{0}{6}\\
=0$
