Answer
$\dfrac{13}{x^{2}-5x+6}-\dfrac{5}{x-3}=\dfrac{23-5x}{(x-3)(x-2)}$
Work Step by Step
$\dfrac{13}{x^{2}-5x+6}-\dfrac{5}{x-3}$
Factor the denominator of the first fraction:
$\dfrac{13}{x^{2}-5x+6}-\dfrac{5}{x-3}=\dfrac{13}{(x-3)(x-2)}-\dfrac{5}{x-3}=...$
Evaluate the substraction of the two rational expressions and simplify:
$...=\dfrac{13-5(x-2)}{(x-3)(x-2)}=\dfrac{13-5x+10}{(x-3)(x-2)}=\dfrac{-5x+23}{(x-3)(x-2)}=...$
$...=\dfrac{23-5x}{(x-3)(x-2)}$