\(\dfrac{16}{x-\dfrac{1}{3}}=\dfrac{x-\dfrac{1}{3}}{4}\left(x\ne\dfrac{1}{3}\right)\\ \Leftrightarrow\left(x-\dfrac{1}{3}\right)^2=16\cdot4=64\\ \Leftrightarrow\left[{}\begin{matrix}x-\dfrac{1}{3}=8\\x-\dfrac{1}{3}=-8\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{25}{3}\\x=-\dfrac{23}{3}\end{matrix}\right.\)