Đáp án:

$\begin{array}{l}
d)Dkxd:x \ne  - 1;y \ne  - 2\\
\left\{ \begin{array}{l}
\frac{1}{{x + 1}} - \frac{2}{{y + 2}} =  - 3\\
\frac{{3x}}{{x + 1}} + \frac{{4y}}{{y + 2}} = 2
\end{array} \right. \Rightarrow \left\{ \begin{array}{l}
\frac{1}{{x + 1}} - \frac{2}{{y + 2}} =  - 3\\
3 - \frac{3}{{x + 1}} + 4 - \frac{8}{{y + 2}} = 2
\end{array} \right.\\
 \Rightarrow \left\{ \begin{array}{l}
\frac{1}{{x + 1}} - 2.\frac{1}{{y + 2}} =  - 3\\
 - 3.\frac{1}{{x + 1}} - 8.\frac{1}{{y + 2}} =  - 5
\end{array} \right.\\
 \Rightarrow \left\{ \begin{array}{l}
\frac{1}{{x + 1}} =  - 1\\
\frac{1}{{y + 2}} = 1
\end{array} \right. \Rightarrow \left\{ \begin{array}{l}
x + 1 =  - 1\\
y + 2 = 1
\end{array} \right.\\
 \Rightarrow \left\{ \begin{array}{l}
x =  - 2\\
y =  - 3
\end{array} \right.\left( {tmdk} \right)\\
e)DKxd:\sqrt 2 x \ne y;x \ne  - y\\
\left\{ \begin{array}{l}
\frac{4}{{\sqrt 2 x - y}} - \frac{{21}}{{x + y}} = \frac{1}{2}\\
\frac{3}{{\sqrt 2 x - y}} + \frac{{7 - x - y}}{{x + y}} = 1
\end{array} \right.\\
 \Rightarrow \left\{ \begin{array}{l}
4.\frac{1}{{\sqrt 2 x - y}} - 21.\frac{1}{{x + y}} = \frac{1}{2}\\
3.\frac{1}{{\sqrt 2 x - y}} + \frac{7}{{x + y}} - 1 = 1
\end{array} \right.\\
 \Rightarrow \left\{ \begin{array}{l}
4.\frac{1}{{\sqrt 2 x - y}} - 21.\frac{1}{{x + y}} = \frac{1}{2}\\
3.\frac{1}{{\sqrt 2 x - y}} + 7.\frac{1}{{x + y}} = 2
\end{array} \right.\\
 \Rightarrow \left\{ \begin{array}{l}
\frac{1}{{\sqrt 2 x - y}} = \frac{1}{2}\\
\frac{1}{{x + y}} = \frac{1}{{14}}
\end{array} \right.\\
 \Rightarrow \left\{ \begin{array}{l}
\sqrt 2 x - y = 2\\
x + y = 14
\end{array} \right.\\
 \Rightarrow \left\{ \begin{array}{l}
x = \frac{{16}}{{\sqrt 2  + 1}} = 16\sqrt 2  - 16\\
y = 30 - 16\sqrt 2 
\end{array} \right.
\end{array}$