2. Find all pairs of numbers $(a, b)$ for which the function

$$
f(x)=\frac{(2 a+3 b) x+a+2 b}{a x+b}
$$

is constant over its entire domain of definition.

(7 points)
Answer: $a= \pm \sqrt{3} b, b \neq 0$.

Solution: a similar solution to this problem is present in Variant 1 under the same number.