$$\begin{gathered} \mathrm{If} \frac{8}{{\left(\mathrm{x}+3\right)}^2\left(\mathrm{x}-2\right)}=\frac{\mathrm{Ax}}{{\left(\mathrm{x}+3\right)}^2}+\frac{\mathrm{C}}{\mathrm{x}-2} \mathrm{then} \\ 25\left(\mathrm{B}+8\mathrm{C}-\mathrm{A}\right)= \end{gathered}$$

$\begin{array}{rcl}\frac{8}{{(\mathrm{x}+3)}^2(\mathrm{x}-2)}& =& \frac{\mathrm{Ax}+\mathrm{B}}{{(\mathrm{x}+3)}^2}+\frac{\mathrm{C}}{\mathrm{x}-2}\\ 8& =& (\mathrm{Ax}+\mathrm{B})(\mathrm{x}-2)+\mathrm{C}{(\mathrm{x}+3)}^2 \mathrm{x}=2 \Rightarrow 8=25 \mathrm{C}\Rightarrow \mathrm{C}=\frac{8}{25}\end{array}$

constant

 $$\begin{gathered} \Rightarrow 8=-2\mathrm{B}+9\mathrm{C} \\ \Rightarrow 8-\frac{72}{25}=-2\mathrm{B} \\ \frac{28}{25}=-2\mathrm{B}\Rightarrow \mathrm{B}=\frac{-64}{25} \end{gathered}$$

$\begin{array}{rcl}{\mathrm{x}}^2 \mathrm{coeff}& \Rightarrow & \mathrm{O}=\mathrm{A}+\mathrm{C}\\ \mathrm{A}& =& \frac{-8}{25}\\ 25(\mathrm{B}+8\mathrm{C}-\mathrm{A})& =& 25\left(\frac{64-64+8}{25}\right)\\ & =& 8\end{array}$