AMC 10A 2019 Problem 24

Let p, q, and r be the distinct roots of the polynomial x^{3}-22 x^{2}+ 80 x-67. There exist real numbers A, B, and C such that

\dfrac{1}{s^{3}-22 s^{2}+80 s-67}=\dfrac{A}{s-p}+\dfrac{B}{s-q}+\dfrac{C}{s-r}

for all real numbers s with s \notin\{p, q, r\}. What is \dfrac{1}{A}+\dfrac{1}{B}+\dfrac{1}{C} ?

Answer Choices
A. 243
B. 244
C. 245
D. 246
E. 247