\(3-\frac{1-\frac{1}{3}}{1+\frac{1}{x}}=2\frac{2}{3}\)
\(\Rightarrow\frac{1}{3}-\frac{2}{3}:\left(1+\frac{1}{x}\right)=0\)
\(\Rightarrow\frac{1}{3}-\frac{2}{3}:\frac{x+1}{x}=0\)
\(\Rightarrow\frac{2}{3}.\frac{x}{x+1}=\frac{1}{3}\)
\(\Rightarrow\frac{2x}{3x+3}=\frac{1}{3}\)
\(\Rightarrow6x=3x+3\)
\(\Rightarrow x=1\)
\(3-\frac{1-\frac{1}{3}}{1+\frac{1}{x}}=2\frac{2}{3}\)\(\Rightarrow\left(1-\frac{1}{3}\right):\left(1+\frac{1}{x}\right)=3-2\frac{2}{3}\)\(\Rightarrow\frac{2}{3}:\left(1+\frac{1}{x}\right)=\frac{1}{3}\)\(\Rightarrow1+\frac{1}{x}=\frac{2}{3}:\frac{1}{3}\)\(\Rightarrow1+\frac{1}{x}=2\)\(\Rightarrow\frac{1}{x}=2-1\)\(\Rightarrow\frac{1}{x}=1\)\(\Rightarrow\frac{1}{x}=\frac{1}{1}\)\(\Rightarrow x=1\)
