\(23+\frac{x}{47-x}=\frac{2}{3}\)
\(\frac{x}{47-x}=\frac{-67}{3}\)\(\Rightarrow\orbr{\begin{cases}x=-67\\47-x=3\Rightarrow x=44\end{cases}}\)
\(23-\frac{x}{47+x}=\frac{1}{3}\)
\(\frac{x}{47+x}=\frac{68}{3}\)\(\Rightarrow\orbr{\begin{cases}x=68\\47+x=3\Rightarrow x=-44\end{cases}}\)