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Question
Resolve into Partial Fractions:
`(x - 4)/(x^2 - 3x + 2)`
Solution
`(x - 4)/(x^2 - 3x + 2) = (x - 4)/((x - 1)(x - 2))`
`=> (x - 4)/(x^2 - 3x + 2) = "A"/(x - 1) + "B"/(x - 2)`
⇒ x - 4 = A(x - 2) + B(x - 1) ....(1)
Substituting x = 1 in (1) we get,
∴ 1 - 4 = A(1 - 2) + B(1 - 1)
⇒ - 3 = A(- 1) + B(0)
⇒ - 3 = A(-1)
⇒ A = 3
Substituting x = 2 in (1) we get,
∴ x - 4 = A(x - 2) + B(x - 1)
⇒ 2 - 4 = A(2 - 2) + B(2 - 1)
⇒ - 2 = A(0) + B(1)
⇒ - 2 = B
∴ `(x - 4)/(x^2 - 3x + 2) = 3/(x - 1) - 2/(x - 2)`
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