$\dfrac{24}{x}-\dfrac{24}{x+4}=\dfrac{1}{2}\,\,\,(x\ne0;\,x\ne-4)\\⇔24\times2(x+4)-24\times2x=x(x+4)\\⇔48(x+4)-48x=x^2+4x\\⇔48x+192-48x=x^2+4x\\⇔x^2+4x-192=0\\⇔x^2+16x-12x-192=0\\⇔x(x+16)-12(x+16)=0\\⇔(x+16)(x-12)=0\\⇔\left[\begin{array}{}x+16=0\\x-12=0\end{array}\right.\\⇔\left[\begin{array}{}x=-16\\\hspace{-0,4cm}x=12\end{array}\right.\text{ (thoả mãn)}$
