Bài giải:

$\frac{a}{x+1}+\frac{b}{x-2}=\frac{32x-19}{{{x}^{2}}-x-2}$

$\frac{a(x-2)}{(x+1)(x-2)}$ + $\frac{b(x+1)}{(x-2)(x+1)}$ = $\frac{32x-19}{(x-2)(x+1)}$

a (x – 2) + b(x + 1) = 32x – 19

ax – 2a + bx + b = 32x – 19

x(a + b) + (-2a + b) = 32x – 19

Suy ra: $\left\{ \begin{align}& a+b=32 \\ & -2a+b=-19 \\ \end{align} \right.$

$\Rightarrow $ $\left\{ \begin{align}& a=32-b \\ & -2(32-b)+b=-19 \\ \end{align} \right.$

$\Rightarrow $$\left\{ \begin{align}& a=32-b \\ & 3b=45 \\ \end{align} \right.$

$\Rightarrow $$\left\{ \begin{align}& a=17 \\ & b=15 \\ \end{align} \right.$

Suy ra tích a.b là: 17. 15 = 255

Vậy đáp án đúng là: C.