$\displaystyle s+9/((s^2)-14s+49)$ can be factored as (s+9)/(s-7)(s-7)..
$\displaystyle (s+9)/(s-7)^2=A(s-7)+B(s-7)$
2. $\displaystyle \frac{{s + 9}} {{(s - 7)^2 }} = \frac{{(s - 7) + 16}} {{(s - 7)^2 }} = \frac{1} {{s - 7}} + \frac{{16}} {{(s - 7)^2 }}.$