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Question: Write the terms for the partial fraction decomposition of 9x2-1.


A ) Ax + 1 - Bx -1
B ) Ax + 1 + Bx2 -1
C ) Ax + 1 + Bx +1
D ) Ax + 1 + Bx -1

Steps to derive

1 9x2 -1 = 9(x + 1)(x -1)
 [Factor the denominator.]

2 9(x + 1)(x -1) = Ax + 1 + Bx -1.
 [Write the partial fraction decomposition with the distinct linear factors.]



Hence the right answer is Option D

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