Đáp án:

$\begin{array}{l}
a)Dk:x \ne  - 7\\
\dfrac{{2x - 5}}{{x + 7}} = \dfrac{1}{4}\\
 \Leftrightarrow x + 7 = 4.\left( {2x - 5} \right)\\
 \Leftrightarrow x + 7 = 8x - 20\\
 \Leftrightarrow 7x = 27\\
 \Leftrightarrow x = \dfrac{{27}}{7}\left( {tm} \right)\\
Vậy\,x = \dfrac{{27}}{7}\\
b)\dfrac{{3x + 7}}{2} = \dfrac{{15x}}{4}\\
 \Leftrightarrow 2.\left( {3x + 7} \right) = 15x\\
 \Leftrightarrow 6x + 14 = 15x\\
 \Leftrightarrow 15x - 6x = 14\\
 \Leftrightarrow 9x = 14\\
 \Leftrightarrow x = \dfrac{{14}}{9}\\
Vậy\,x = \dfrac{{14}}{9}\\
c)\dfrac{{2 - 3x}}{5} = \dfrac{{x + 1}}{3}\\
 \Leftrightarrow 3.\left( {2 - 3x} \right) = 5.\left( {x + 1} \right)\\
 \Leftrightarrow 6 - 9x = 5x + 5\\
 \Leftrightarrow 5x + 9x = 6 - 5\\
 \Leftrightarrow 14x = 1\\
 \Leftrightarrow x = \dfrac{1}{{14}}\\
Vậy\,x = \dfrac{1}{{14}}\\
d)Dkxd:x \ne 2;x \ne  - 6\\
\dfrac{4}{{x - 2}} = \dfrac{5}{{x + 6}}\\
 \Leftrightarrow 4.\left( {x + 6} \right) = 5.\left( {x - 2} \right)\\
 \Leftrightarrow 4x + 24 = 5x - 10\\
 \Leftrightarrow 5x - 4x = 24 + 10\\
 \Leftrightarrow x = 34\left( {tm} \right)\\
Vậy\,x = 34
\end{array}$