Answer
$\frac{2}{x-3}+\frac{3}{x-2}$
Work Step by Step
The form of the partial fraction decomposition is
$\frac{5x-13}{(x-3)(x-2)}=\frac{A}{x-3}+\frac{B}{x-2}$
$⇒5x-13= A(x-2)+B(x-3)$
Equating the coefficients of x and the constant term, we get
A+B=5 and 2A+3B=13.
Solving these equations, we get A=2 and B=3.
Thus, $\frac{5x-13}{(x-3)(x-2)}=\frac{2}{x-3}+\frac{3}{x-2}$
