\(\frac{4+\frac{4}{17}+\frac{4}{19}+\frac{4}{2003}}{5+\frac{5}{17}+\frac{5}{19}+\frac{5}{2003}}\)
= \(\frac{4.\left(1+\frac{1}{17}+\frac{1}{19}+\frac{1}{2003}\right)}{5.\left(1+\frac{1}{17}+\frac{1}{19}+\frac{1}{2003}\right)}\)
= \(\frac{4}{5}\)
\(\frac{4+\frac{4}{17}+\frac{4}{19}+\frac{4}{2003}}{5+\frac{5}{17}+\frac{5}{19}+\frac{5}{2003}}=\frac{4\left(1+\frac{1}{17}+\frac{1}{19}+\frac{1}{2003}\right)}{5\left(1+\frac{1}{17}+\frac{1}{19}+\frac{1}{2003}\right)}=\frac{4}{5}\)
\(\frac{4+\frac{4}{17}+\frac{4}{19}+\frac{4}{2003}}{5+\frac{5}{17}+\frac{5}{19}+\frac{5}{2003}}\)
\(=\frac{4.(\frac{1}{17}+\frac{1}{19}+\frac{1}{2003})}{5.(\frac{1}{17}+\frac{1}{19}+\frac{1}{2003})}\)
\(=\frac{4}{5}\)