#andy

\[\begin{array}{l}
\dfrac{{72}}{{x - 4}} - \dfrac{{80}}{{x + 4}} = \dfrac{1}{4}\\
DKXD:\left\{ \begin{array}{l}
x - 4 \ne 0\\
x + 4 \ne 0
\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}
x \ne 4\\
x \ne  - 4
\end{array} \right.\\
 \Leftrightarrow MC:4\left( {x - 4} \right)\left( {x + 4} \right)\\
 \Leftrightarrow \dfrac{{72.4.\left( {x + 4} \right)}}{{4\left( {x - 4} \right)\left( {x + 4} \right)}} - \dfrac{{80.4.\left( {x - 4} \right)}}{{4\left( {x - 4} \right)\left( {x + 4} \right)}} = \dfrac{{\left( {x - 4} \right)\left( {x + 4} \right)}}{{4\left( {x - 4} \right)\left( {x + 4} \right)}}\\
 \Rightarrow 288\left( {x + 4} \right) - 320\left( {x - 4} \right) = \left( {x - 4} \right)\left( {x + 4} \right)\\
 \Leftrightarrow 1152 + 288x - 320x + 1280 = {x^2} - 16\\
 \Leftrightarrow  - 32x + 1152 + 1280 = {x^2} - 16\\
 \Leftrightarrow  - 32x + 2432 = {x^2} - 16\\
 \Leftrightarrow  - 32x + 2432 - {x^2} + 16 = 0\\
 \Leftrightarrow  - 32x + 2448 - {x^2} = 0\\
 \Leftrightarrow  - {x^2} - 32x + 2448 = 0\\
 \Leftrightarrow  - {x^2} + 36x - 68x + 2448 = 0\\
 \Leftrightarrow \left( { - {x^2} + 36x} \right) + \left( { - 68x + 2448} \right) = 0\\
 \Leftrightarrow x\left( { - x + 36} \right) + 68\left( { - x + 36} \right) = 0\\
 \Leftrightarrow \left( { - x + 36} \right)\left( {x + 68} \right) = 0\\
 \Leftrightarrow \left[ \begin{array}{l}
 - x + 36 = 0\\
x + 68 = 0
\end{array} \right.\\
 \Leftrightarrow \left[ \begin{array}{l}
x = 36\\
x =  - 68
\end{array} \right.\\
 \Rightarrow S = \left\{ {36; - 68} \right\}
\end{array}\]

Đáp án:

 #Clickbim 

`72/(x-4) - 80/(x+4) = 1/4 (ĐK: x \ne 4 ; x \ne -4)`

`<=> [72.4(x+4)]/[4(x-4)(x+4)] - [80.4(x-4)]/[4(x-4)(x+4)] = [(x-4)(x+4)]/[4(x-1)(x+1)]`

`-> 288x + 1152 - 320x + 1280 = x^2 - 16`

`<=> (288x - 320x) + (1152 + 1280) = x^2 - 16`

`<=> -32x + 2432 = x^2 - 16`

`<=> -32x + 2432 - x^2 + 16 = 0`

`<=> -x^2 - 32x + (2432 + 16) = 0 `

`<=> -x^2 - 32x + 2448 = 0`

`<=> -x^2 + 36x - 68x  + 2448 = 0`

`<=> (-x^2 + 36x) + (-68x + 2448) = 0`

`<=> x(-x+36) + 68(-x+36) = 0`

`<=> (x+68)(-x+26) = 0`

`<=>` $\left[\begin{matrix} x+68=0\\ -x+36=0\end{matrix}\right.$

`<=>` $\left[\begin{matrix} x=-68\\ x=36\end{matrix}\right.$

Vậy `S = {-68;36}`

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