Resposta:

5,5454... - 4,1212...=

[tex]5,5454...=\dfrac{554-4}{99}=\dfrac{549}{99}\\ \\ simplificando\\ \\ \dfrac{549:3}{99:3}=\boxed{\dfrac{183}{33}}[/tex]

[tex]4,1212...=\dfrac{412-4}{99}=\dfrac{408}{99}\\ \\ simplificando\\ \\ \dfrac{408:3}{99:3}=\boxed{\dfrac{136}{33}}[/tex]

Resolvendo a expressão

[tex]\dfrac{183}{33}-\dfrac{136}{33}=\boxed{\dfrac{47}{33}}[/tex]