[tex]\displaystyle \\
\frac{\overline{abab}}{\overline{cdcd}} = \frac{1000a+100b+10a+b}{1000c+100d+10c+d} = \frac{1010a+101b}{1010c+101d} = \\ \\ \\
= \frac{101\times10a+101b}{101\times10c+101d} = \frac{101(10a+b)}{101(10c+d)} =\frac{10a+b}{10c+d} = \boxed{\frac{\overline{ab}}
{\overline{cd}} } \\ \\ \\
\Longrightarrow~~\boxed{\frac{\overline{ab}}{\overline{cd}} =\frac{\overline{abab}}{\overline{cdcd}} } [/tex]
