Question

Resolve 9/((x - 1)(x + 2)2) into the partial fraction.

Answer 1

Let 9/((x - 1)(x+ 2)2) = A/(x - 1) + B/(x + 2) + C/(x + 2)2

Multiplying with (x –1) (x + 2)2

9 = A (x + 2)2 + B(x – 1) (x + 2) + C(x – 1) x = 1

⇒ 9 = 9A ⇒ A = 1

x = –2 ⇒ 9 = –3C ⇒ C = –3

Equating the coefficients of x2

A + B = 0 ⇒ B = – A = –1

∴ 9/((x - 1)(x + 2)2) = 1/(x - 1) - 1/(x + 2) - 3/(x + 2)2