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Question
Resolve into Partial Fractions:
`(5x + 7)/((x-1)(x+3))`
Solution
`(5x + 7)/((x-1)(x+3)) = "A"/(x-1) + "B"/(x+3)`
⇒ 5x + 7 = A(x + 3) +B(x - 1) ...(1)
Substituting x = 1 in (1) we get,
5(1) + 7 = A(1 + 3) +B(1 - 1)
⇒ 12 = A(4)
⇒ `12/4` = 3
⇒ A = 3` .....(1)
Substituting x = - 3 in (1) we get,
5(-3) + 7 = A(- 3 + 3) +B(- 3 - 1)
⇒ - 8 = B(-4)
⇒ B = `(-8)/(-4)`
⇒ B = 2
∴ `(5x + 7)/((x-1)(x+3)) = 3/(x - 1) + 2/(x + 3)`
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