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

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

Answer»

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

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

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