1. (10 points) Calculate: $2017 \frac{2016}{2017} \div 2019 \frac{1}{2016}+\frac{1}{2017}=$ $\qquad$
1. (10 points) Calculate: $2017 \frac{2016}{2017} \div 2019 \frac{1}{2016}+\frac{1}{2017}=$ $\qquad$ .

【Analysis】First convert the mixed numbers to improper fractions, then simplify the numerator for easier calculation.
【Solution】Solution: $2017 \frac{2016}{2017} \div 2019 \frac{1}{2016}+\frac{1}{2017}$
$$
\begin{array}{l}
=\frac{2017^{2}+2016}{2017} \div \frac{2016 \times 2019+1}{2016}+\frac{1}{2017} \\
=\frac{(2016+1) \times(2018-1)+2016}{2017} \div \frac{2016 \times(2018+1)+1}{2016}+\frac{1}{2017} \\
=\frac{2016 \times 2018+1+2016}{2017} \div \frac{2016 \times 2018+2016+1}{2016}+\frac{1}{2017} \\
=\frac{2016}{2017}+\frac{1}{2017} \\
=1
\end{array}
$$

Therefore, the answer is: 1.