Đáp án:
$1)
a)0\\
b)\dfrac{-621}{551}\\
c)0\\
d) 1\\
e)0\\
f)\dfrac{55}{56}\\
2)
a) x=1\\
b)
x=\dfrac{22}{15}\\
c)
x=-1\\
d) {\left[\begin{aligned}x=\dfrac{9}{8}\\x=-\dfrac{15}{8}\end{aligned}\right.}\\$
Giải thích các bước giải:
$1)
a) \left ( \dfrac{5}{6}+\dfrac{-7}{12} \right )-\left ( \dfrac{5}{12}-\dfrac{1}{6} \right )\\
=\dfrac{5}{6}+\dfrac{-7}{12} - \dfrac{5}{12}+\dfrac{1}{6} \\
=\left (\dfrac{5}{6}+\dfrac{1}{6} \right )+\left (\dfrac{-7}{12} - \dfrac{5}{12} \right )\\
=\dfrac{6}{6}+\dfrac{-12}{12}\\
=1-1=0\\
b) \dfrac{3}{11}.\dfrac{7}{29}+\dfrac{7}{29}.\dfrac{8}{11}+\dfrac{-26}{19}\\
=\dfrac{7}{29}.\left ( \dfrac{3}{11}+\dfrac{8}{11} \right )-\dfrac{26}{19}\\
=\dfrac{7}{29}-\dfrac{26}{19}\\
=\dfrac{133}{551}-\dfrac{754}{551}\\
=\dfrac{-621}{551}\\
c) \dfrac{-5}{12}.\dfrac{2}{11}+\dfrac{-5}{12}.\dfrac{9}{11}+\dfrac{5}{12}\\
=\dfrac{-5}{12}.\left ( \dfrac{2}{11}+\dfrac{9}{11} \right )+\dfrac{5}{12}\\
=\dfrac{-5}{12}+\dfrac{5}{12}\\
=0\\
d) \dfrac{-5}{7}.\dfrac{2}{11}+\dfrac{-5}{7}.\dfrac{9}{11}+1\dfrac{5}{7}\\
=\dfrac{-5}{7}.\left ( \dfrac{2}{11}+\dfrac{9}{11} \right )+\dfrac{12}{7}\\
=\dfrac{-5}{7}+\dfrac{12}{7}\\
=\dfrac{7}{7}=1\\
e) \dfrac{-5}{12}.\dfrac{2}{11}+\dfrac{-5}{12}.\dfrac{9}{11}+\dfrac{5}{12}\\
=\dfrac{-5}{12}\left ( \dfrac{2}{11}+\dfrac{9}{11} \right )+\dfrac{5}{12}\\
=\dfrac{-5}{12}+\dfrac{5}{12}\\
=0\\
f)
\dfrac{6}{7}-\dfrac{5}{8}:5+\dfrac{3}{16}.1\dfrac{1}{3}\\
=\dfrac{6}{7}-\dfrac{5}{8}.\dfrac{1}{5}+\dfrac{3}{16}.\dfrac{4}{3}\\
=\dfrac{6}{7}-\dfrac{1}{8}+\dfrac{1}{4}\\
=\dfrac{48}{56}-\dfrac{7}{56}+\dfrac{14}{56}\\
=\dfrac{55}{56}\\
2)
a) x+\dfrac{3}{21}=\dfrac{8}{7}\\
\Leftrightarrow x=\dfrac{8}{7}-\dfrac{3}{21}\\
\Leftrightarrow x=\dfrac{24}{21}-\dfrac{3}{21}\\
\Leftrightarrow x=\dfrac{21}{21}=1\\
b)
x-\dfrac{2}{3}=\dfrac{4}{5}\\
\Leftrightarrow x=\dfrac{4}{5}+\dfrac{2}{3}\\
\Leftrightarrow x=\dfrac{12}{15}+\dfrac{10}{15}\\
\Leftrightarrow x=\dfrac{22}{15}\\
c)
\left ( \dfrac{1}{5}-x \right ).\dfrac{1}{3}=\dfrac{2}{5}\\
\Leftrightarrow \dfrac{1}{5}-x =\dfrac{2}{5}.3=\dfrac{6}{5}\\
\Leftrightarrow x=\dfrac{1}{5}-\dfrac{6}{5}
\Leftrightarrow x=\dfrac{-5}{5}=-1\\
d) \left | x+\dfrac{3}{8} \right |-1=\dfrac{1}{2}\\
\Leftrightarrow \left | x+\dfrac{3}{8} \right |=\dfrac{1}{2}+1=\dfrac{3}{2}\\
\Leftrightarrow {\left[\begin{aligned}x+\dfrac{3}{8}=\dfrac{3}{2}\\x+\dfrac{3}{8}=-\dfrac{3}{2}\end{aligned}\right.}\\
\Leftrightarrow {\left[\begin{aligned}x=\dfrac{3}{2}-\dfrac{3}{8}\\x=-\dfrac{3}{2}-\dfrac{3}{8}\end{aligned}\right.}\\
\Leftrightarrow {\left[\begin{aligned}x=\dfrac{12}{8}-\dfrac{3}{8}\\x=-\dfrac{12}{8}-\dfrac{3}{8}\end{aligned}\right.}\\
\Leftrightarrow {\left[\begin{aligned}x=\dfrac{9}{8}\\x=-\dfrac{15}{8}\end{aligned}\right.}\\$
