\(\frac{1234\times567-667}{567}+1234+566\)
\(=\frac{1234\times567-567-100}{567}+1234+566\)
\(=\frac{1234\times567}{567}-\frac{567}{567}-\frac{100}{567}+1234+566\)
\(=1234-1-\frac{100}{567}+1234+566\)
\(=1234\times2+564+\left(1-\frac{100}{567}\right)\)
\(=3032+\frac{467}{567}=3032\frac{467}{567}\)