#andy

\[\begin{array}{l}
\dfrac{{2 - x}}{9} + \dfrac{{3 - x}}{8} = \dfrac{{4 - x}}{7} + \dfrac{{5 - x}}{6}\\
 \Leftrightarrow \dfrac{{2 - x}}{9} + \dfrac{{3 - x}}{8} - \dfrac{{4 - x}}{7} - \dfrac{{5 - x}}{6} = 0\\
MC:504\\
 \Leftrightarrow 56\left( {2 - x} \right) + 63\left( {3 - x} \right) - 72\left( {4 - x} \right) - 84\left( {5 - x} \right) = 0\\
 \Leftrightarrow 112{\rm{ }} - {\rm{ }}56x + 189{\rm{ }} - {\rm{ }}63x - 288{\rm{ }} - {\rm{ }}72x - 420{\rm{ }} - {\rm{ }}84x = 0\\
 \Leftrightarrow  - 56x - 63x + 72x + 84x = 0 - 112 - 189 + 288 + 420\\
 \Leftrightarrow 37x = 407\\
 \Leftrightarrow x = 407:37\\
 \Leftrightarrow x = 11\\
 \Rightarrow S = \left\{ {11} \right\}
\end{array}\]

Answer

`{2 - x}/9 + {3 - x}/8 = {4 - x}/7 + {5 - x}/6`

`<=> {2 - x}/9 + {3 - x}/8 - {4 - x}/7 - {5 - x}/6 = 0`

`<=> {56 . (2 - x)}/{9 . 56} + {63 . (3 - x)}/{8 . 63} - {72 . (4 - x)}/{7 . 72} - {84 . (5 - x)}/{6 . 84} = 0`

`<=> {112 - 56x}/{504} + {189 - 63x}/{504} - {288 - 72x}/{504} - {420 - 84x}/{504} = 0`

`<=> 112 - 56x + 189 - 63x - 288 + 72x - 420 + 84x = 0` 

`<=> (-56x - 63x + 72x + 84x) + (112 + 189 - 288 - 420) = 0`

`<=> 37x - 407 = 0`

`<=> 37x = 0 + 407`

`<=> 37x = 407`

`<=> x = 407 : 37`

`<=> x = 11`

Vậy `S = {11}`