Đáp án:

 $1)
a)-14\\
b)
\dfrac{1}{9}\\
c)
\dfrac{-13}{66}\\
d)
\dfrac{-3}{5}\\
e)
M=\dfrac{3}{13}\\
2)
a)
 {\left[\begin{aligned}x=-\dfrac{1}{4}\\x=\dfrac{3}{7}\end{aligned}\right.}\\
d)
 x=\dfrac{-3}{2}\\
b)
 x=-5\\
c)
x=-1\\
e)
 x=\dfrac{13}{21}\\
f)
{\left[\begin{aligned}x=0\\x=1\end{aligned}\right.}\\$

Giải thích các bước giải:

 $1)
a) \left ( -\dfrac{5}{11} \right ).\dfrac{7}{15}.\left ( \dfrac{11}{-5} \right ).(-30)\\
=\left (\dfrac{-5}{11}.\dfrac{11}{-5}  \right )\left (\dfrac{7}{15}.15.(-2)  \right )\\
=1.(-14)=-14\\
b)
\left ( \dfrac{-1}{6} \right ).\left ( -\dfrac{15}{19} \right ).\dfrac{38}{45}\\
=\dfrac{1}{6}.\dfrac{15}{19}.\dfrac{2.19}{15.3}\\
=\dfrac{1}{6}.\dfrac{2}{3}\\
=\dfrac{1}{9}\\
c)
\left ( -\dfrac{5}{9} \right ).\dfrac{3}{11}+\left ( -\dfrac{3}{18} \right ).\dfrac{3}{11}\\
=\dfrac{3}{11}.\left ( \dfrac{-5}{9}+\dfrac{-3}{18} \right )\\
=\dfrac{3}{11}.\left ( \dfrac{-10}{18}+\dfrac{-3}{18} \right )\\
=\dfrac{3}{11}.\dfrac{-13}{18}\\
=\dfrac{-13}{66}\\
d)
\left ( 2\dfrac{2}{15}.\dfrac{9}{17}.\dfrac{3}{32} \right ):\left ( -\dfrac{3}{17} \right )\\
=\dfrac{32}{15}.\dfrac{9}{17}.\dfrac{3}{32} .\dfrac{-17}{3} \\
=\left ( \dfrac{32}{15}.\dfrac{3}{32}  \right ).\left (\dfrac{9}{17}.\dfrac{-17}{3}   \right )\\
=\dfrac{1}{5}.(-3)\\
=\dfrac{-3}{5}\\
e)
M=\dfrac{\dfrac{3}{4}-\dfrac{3}{5}+\dfrac{3}{7}+\dfrac{3}{11}}{\dfrac{13}{4}-\dfrac{13}{5}+\dfrac{13}{7}+\dfrac{13}{11}}\\
=\dfrac{3.\left (\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{7}+\dfrac{1}{11}  \right )}{13.\left (\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{7}+\dfrac{1}{11}  \right )}\\
=\dfrac{3}{13}\\
2)
a)
\left ( x+\dfrac{1}{4} \right ).\left ( x-\dfrac{3}{7} \right )=0\\
\Leftrightarrow {\left[\begin{aligned}x+\dfrac{1}{4}=0\\x-\dfrac{3}{7}=0\end{aligned}\right.}\\
\Leftrightarrow {\left[\begin{aligned}x=-\dfrac{1}{4}\\x=\dfrac{3}{7}\end{aligned}\right.}\\
d)
\left ( \dfrac{2x}{3}-3 \right ):(-10)=\dfrac{2}{5}\\
\Leftrightarrow \dfrac{2x}{3}-3=\dfrac{2}{5}.(-10)=-4\\
\Leftrightarrow \dfrac{2x}{3}=-4+3=-1\\
\Leftrightarrow x=\dfrac{-3}{2}\\
b)
\dfrac{2}{3}+\dfrac{1}{3}:x=\dfrac{3}{5}\\
\Leftrightarrow \dfrac{1}{3}:x=\dfrac{3}{5}-\dfrac{2}{3}\\
\Leftrightarrow \dfrac{1}{3}:x=\dfrac{9}{15}-\dfrac{10}{15}\\
\Leftrightarrow \dfrac{1}{3}.\dfrac{1}{x}=\dfrac{-1}{15}\\
\Leftrightarrow \dfrac{1}{x}=\dfrac{-1}{15}.3=\dfrac{-1}{5}\\
\Leftrightarrow x=-5\\
c)
1,5x-2\dfrac{1}{3}x=1,5-\dfrac{2}{3}\\
\Leftrightarrow \dfrac{3}{2}x-\dfrac{7}{3}x=\dfrac{3}{2}-\dfrac{2}{3}\\
\Leftrightarrow \left (\dfrac{9}{6}-\dfrac{14}{6}  \right )x=\dfrac{9}{6}-\dfrac{4}{6}\\
\Leftrightarrow -\dfrac{5}{6}  x=\dfrac{5}{6}\\
\Leftrightarrow x=\dfrac{5}{6}.\dfrac{-6}{5}=-1\\
e)
-\dfrac{21}{13}x+\dfrac{1}{3}=\dfrac{-2}{3}\\
\Leftrightarrow -\dfrac{21}{13}x=\dfrac{-2}{3}-\dfrac{1}{3}\\
\Leftrightarrow -\dfrac{21}{13}x=\dfrac{-3}{3}=-1\\
\Leftrightarrow x=\dfrac{13}{21}\\
f)
x.x=x-x.x-x\\
\Leftrightarrow 2x^2=2x=0\\
\Leftrightarrow 2x(x-1)=0\\
\Leftrightarrow {\left[\begin{aligned}x=0\\x=1\end{aligned}\right.}\\$