\(\Leftrightarrow\dfrac{1}{x+\dfrac{1}{\dfrac{x-3-x-1}{x-3}}}=4\)
\(\Leftrightarrow\dfrac{1}{x+1:\dfrac{-2}{x-3}}=4\)
\(\Leftrightarrow\dfrac{1}{x-\dfrac{x-3}{2}}=4\)
\(\Leftrightarrow\dfrac{1}{\dfrac{2x-x+3}{2}}=4\)
\(\Leftrightarrow\dfrac{2}{x+3}=4\)
\(\Leftrightarrow x=-\dfrac{5}{2}\)