AMO 2025 Secondary 3 (Grade 9) Question 2

Positive integers $A,B$ satisfy $\frac A{x+2}+\frac B{x-3}=\frac{45x-10}{x^2-x-6}$. Find $A+B$. Clarification: interpret the equality as an identity for every $x\ne-2,3$; the source does not explicitly state this.