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प्रश्न
Resolve into partial fraction for the following:
`(4x + 1)/((x - 2)(x + 1))`
उत्तर
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)`
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