Đáp án:

$\begin{array}{l}
a)Dkxd:x \ne 0;x \ne 2\\
B = \left( {\dfrac{{x - 4}}{{x.\left( {x - 2} \right)}} + \dfrac{2}{{x - 2}}} \right):\left( {\dfrac{{x + 2}}{x} - \dfrac{x}{{x - 2}}} \right)\\
 = \dfrac{{x - 4 + 2x}}{{x\left( {x - 2} \right)}}:\dfrac{{\left( {x + 2} \right)\left( {x - 2} \right) - {x^2}}}{{x\left( {x - 2} \right)}}\\
 = \dfrac{{3x - 4}}{{x\left( {x - 2} \right)}}.\dfrac{{x\left( {x - 2} \right)}}{{{x^2} - 4 - {x^2}}}\\
 = \dfrac{{3x - 4}}{{ - 4}}\\
 = \dfrac{{4 - 3x}}{4}\\
b)x =  - 2\left( {tmdk} \right)\\
 \Rightarrow B = \dfrac{{4 - 3x}}{4} = \dfrac{{4 - 3.\left( { - 2} \right)}}{4} = \dfrac{5}{2}\\
c)\left| B \right| - 2x = 5\\
 \Rightarrow \left| B \right| = 2x + 5\\
 \Rightarrow \left[ \begin{array}{l}
B = 2x + 5\\
B =  - 2x - 5
\end{array} \right.\\
 \Rightarrow \left[ \begin{array}{l}
\dfrac{{4 - 3x}}{4} = 2x + 5\\
\dfrac{{4 - 3x}}{4} =  - 2x - 5
\end{array} \right.\\
 \Rightarrow \left[ \begin{array}{l}
4 - 3x = 8x + 20\\
4 - 3x =  - 8x - 20
\end{array} \right.\\
 \Rightarrow \left[ \begin{array}{l}
11x =  - 16\\
5x =  - 24
\end{array} \right.\\
 \Rightarrow \left[ \begin{array}{l}
x =  - \dfrac{{16}}{{11}}\\
x =  - \dfrac{{24}}{5}
\end{array} \right.\left( {tmdk} \right)\\
d)\left( {2 - x} \right).B\\
 = \left( {2 - x} \right).\dfrac{{4 - 3x}}{4}\\
 = \dfrac{{\left( {x - 2} \right).\left( {3x - 4} \right)}}{4}\\
 = \dfrac{1}{4}.\left( {3{x^2} - 10x + 8} \right)\\
 = \dfrac{1}{4}.3.\left( {{x^2} - 2.x.\dfrac{5}{3} + \dfrac{{25}}{9} - \dfrac{{25}}{9} + \dfrac{8}{3}} \right)\\
 = \dfrac{3}{4}.{\left( {x - \dfrac{5}{3}} \right)^2} - \dfrac{1}{{12}} \ge  - \dfrac{1}{{12}}\\
 \Rightarrow GTNN:\left( {2 - x} \right).B =  - \dfrac{1}{{12}}\,khi:x = \dfrac{5}{3}\\
e)B = \dfrac{{4 - 3x}}{4} = 1 - \dfrac{3}{4}x\\
B =  - 1\\
 \Rightarrow 1 - \dfrac{3}{4}x =  - 1\\
 \Rightarrow \dfrac{3}{4}x = 2\\
 \Rightarrow x = \dfrac{8}{3}\left( {tmdk} \right)\\
g)\left| B \right| + 3 < 2x - 1\\
 \Rightarrow \left| B \right| < 2x - 4\\
 \Rightarrow \left| {\dfrac{{4 - 3x}}{4}} \right| < 2x - 4\\
 \Rightarrow \left| {3x - 4} \right| < 8x - 16\\
 \Rightarrow \left\{ \begin{array}{l}
3x - 4 < 8x - 16\\
3x - 4 >  - 8x + 16
\end{array} \right.\\
 \Rightarrow \left\{ \begin{array}{l}
4x > 12\\
11x > 20
\end{array} \right.\\
 \Rightarrow \left\{ \begin{array}{l}
x > 3\\
x > \dfrac{{20}}{{11}}
\end{array} \right.\\
 \Rightarrow x > 3
\end{array}$