[tex]\large\boxed{\begin{array}{l}\sf x=4,01313\dotsc\cdot10\\\sf 10x=40,1313\dotsc\cdot100\\\sf 1000x=4013,131313\dotsc\\-\underline{\begin{cases}\sf 1000x=4013,131313\dotsc\\\sf10x=40,131313\end{cases}}\\\sf 990x=3973\\\boxed{\boxed{\boxed{\boxed{\sf x=\dfrac{3973}{990}}}}}\end{array}}[/tex]