Answer
$$A=-3$$ $$B=5$$
Work Step by Step
$\frac{2x-3}{(x-3)(x-4)}$ = $\frac{A}{x-3}$ + $\frac{B}{x-4}$
Multiplying (x-3)(x-4) on both sides, we have:
$2x-3=A(x-4)+B(x-3)$
If we let x=4 on both sides, we can eliminate constant A to find constant B:
$8-3=A(4-4)+B(4-3)$
Thus, $B = 5$.
Similarly, if we let x = 3 on both sides, we can eliminate constant B to find constant A:
$6-3=A(3-4)+B(3-3)$
Thus, $3=-A$ and so $A = -3$.
