1. **State the problem:** Given the equation $$\frac{A}{x+2} + \frac{B}{x-3} = \frac{5x}{(x+2)(x-3)}$$ find the values of constants $A$ and $B$. 2. **Formula and approach:** To solve for $A$ and $B$, multiply both sides by the common denominator $(x+2)(x-3)$ to clear the fractions: $$A(x-3) + B(x+2) = 5x$$ 3. **Expand and simplify:** $$Ax - 3A + Bx + 2B = 5x$$ Group like terms: $$(A + B)x + (-3A + 2B) = 5x + 0$$ 4. **Equate coefficients:** For the equation to hold for all $x$, the coefficients of $x$ and the constant terms must be equal: $$A + B = 5$$ $$-3A + 2B = 0$$ 5. **Solve the system:** From the second equation: $$-3A + 2B = 0 \implies 2B = 3A \implies B = \frac{3}{2}A$$ Substitute into the first equation: $$A + \frac{3}{2}A = 5 \implies \frac{5}{2}A = 5 \implies A = 2$$ Then, $$B = \frac{3}{2} \times 2 = 3$$ 6. **Final answer:** $$A = 2, \quad B = 3$$ This corresponds to option c.