Question

Expand 1/x^2-4 using partial fraction decomposition

Answer 1

1 / X² -4 = (- 1/4) / (X+2) + (1/4) / (X - 2)

Explanation:

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Answer 2

1 / X² -4 = (- 1/4) / (X+2) + (1/4) / (X - 2)

Explanation:

1 / x²-4 = 1 / (X+2) * (X-2)

1 / X²-4 = (A / X+2) + (B / X-2) = (AX - 2A + BX +2B) / X² -4

∴ 1 = (A + B) * X - 2 (A - B)

A + B = 0

- 2 (A - B) = 1

A - B = - 1/2

∴ 2A = - 1/2

A= - 1/4

B= 1/4

1 / X² -4 = (- 1/4) / (X+2) + (1/4) / (X - 2)