If 8x+32x-2=Axx+32+Cx-2 then 25B+8C-A=

8(x+3)2(x-2)=Ax+B(x+3)2+Cx-28=(Ax+B)(x-2)+C(x+3)2 x=2 ⇒ 8=25 C⇒C=825constant ⇒8=-2B+9C ⇒8-7225=-2B 2825=-2B⇒B=-6425x2 coeff⇒O=A+C A=-82525(B+8C-A)=2564-64+825 =8

If 8x+32x-2=Axx+32+Cx-2 then 25B+8C-A=

8(x+3)2(x-2)=Ax+B(x+3)2+Cx-28=(Ax+B)(x-2)+C(x+3)2 x=2 ⇒ 8=25 C⇒C=825constant ⇒8=-2B+9C ⇒8-7225=-2B 2825=-2B⇒B=-6425x2 coeff⇒O=A+C A=-82525(B+8C-A)=2564-64+825 =8

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$If \frac{8}{{(x + 3)}^{2} (x - 2)} = \frac{Ax}{{(x + 3)}^{2}} + \frac{C}{x - 2} then 25 (B + 8 C - A) =$

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Detailed Solution

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

constant

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

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