## Task B-1.1.

Calculate

$$
\frac{20182019^{2}-20182018^{2}}{20182018 \cdot 20182020-20182017 \cdot 20182019}
$$
## Solution.

Let's introduce the substitution $x=20182018$.

Then we have

$$
\begin{array}{cc}
\frac{(x+1)^{2}-x^{2}}{x \cdot(x+2)-(x-1)(x+1)} & 2 \text { points } \\
=\frac{2 x+1}{x^{2}+2 x-x^{2}+1} & 2 \text { points } \\
=\frac{2 x+1}{2 x+1}=1 . & 1 \text { point }
\end{array}
$$