B3. Let $a$ and $b$ be real numbers such that $\frac{a^{2}}{1+a^{2}}+\frac{b^{2}}{1+b^{2}}=1$. Determine all possible values of the expression

$$
(a+b)\left(\frac{a}{1+a^{2}}+\frac{b}{1+b^{2}}\right)
$$

## Problems for 2nd Year

Time for solving: 120 minutes. In section A, we will award two points for the correct answer and deduct one point for an incorrect answer. Write your answers for section A in the left table, leave the right table blank.
![](https://cdn.mathpix.com/cropped/2024_06_07_58dcb28c79ea4cc315e1g-06.jpg?height=168&width=802&top_left_y=647&top_left_x=640)