Question: If $\frac{9}{(x - 1)(x + 2)^{2}} = \frac{A}{x - 1} + \frac{B}{x + 2} + \frac{C}{(x + 2)^{2}}$ then...

Question

If $\frac{9}{(x - 1)(x + 2)^{2}} = \frac{A}{x - 1} + \frac{B}{x + 2} + \frac{C}{(x + 2)^{2}}$ then $A - B - C =$

Answer 1

9 = $A(x + 2)^{2} + B(x - 1)(x + 2) + C(x - 1)$

For $x = 1,9 = 9A \Rightarrow A = 1$

For $x = - 2,9 = - 3C \Rightarrow C = - 3$

Equating coefficient of $x^{2},0 = A + B \Rightarrow B = - A = - 1$

$\therefore$ $A - B - C = 1 - ( - 1) - ( - 3) = 1 + 1 + 3 = 5$ .

Question: If \(\frac{9}{(x - 1)(x + 2)^{2}} = \frac{A}{x - 1} + \frac{B}{x + 2} + \frac{C}{(x + 2)^{2}}\) then...