Question

Resolve into partial fraction for the following:

`(4x + 1)/((x - 2)(x + 1))`

Answer 1

Let `(4x + 1)/((x - 2)(x + 1)) = "A"/(x - 2) + "B"/(x + 1)`  .....(1)

Multiply both sides by (x – 2) (x + 1) we get

4x + 1 = A(x + 1) + B(x – 2) ……. (2)

Put x = -1 in (2) we get

4(-1) + 1 = A(-1 + 1) + B(-1 – 2)

-4 + 1 = A(0) + B(-3)

-3 = B(-3)

B = `(-3)/(-3)` = 1

Put x = 2 in (2) we get

4(2) + 1 = A(2 + 1) + B(2 – 2)

8 + 1 = A(3) + B(0)

9 = 3A

A = 3

Using A = 3, B = 1 in (1) we get

`(4x + 1)/((x - 2)(x + 1)) = 3/(x - 2) + 1/(x + 1)`