[tex]\displaystyle\\
\overline{aa} ~\text{ este un numar prim de 2 cifre egale.}\\
\text{orice numar de 2 cifre egale este divizibil cu numarul 11}\\
\overline{aa} ~\vdots ~11 ~~\text{si}~~\overline{aa} = \text{ numar prim}\\
\Longrightarrow ~~\boxed{\overline{aa} = 11 }\\\\
\frac{3}{55} = \frac{x}{\overline{aa}} \\\\
\frac{3}{55} = \frac{x}{11} \\\\
55x = 3\cdot 11 \\\\
x = \frac{3\cdot 11}{55} \\\\
\boxed{x= \frac{3}{5} }[/tex]
