3. Now, subtract the same positive integer $a$ from the numerator and denominator of the fractions $\frac{2018}{2011}$ and $\frac{2054}{2019}$, respectively, to get two new fractions that are equal. What is the positive integer $a$?
3.2009.

From the given we have
$$
\begin{array}{l}
\frac{2018-a}{2011-a}=\frac{2054-a}{2019-a} \\
\Rightarrow \frac{2018-a}{7}=\frac{2054-a}{35} \\
\Rightarrow a=2009 .
\end{array}
$$