Which of the following equations describes the partial fraction decomposition of a rational function of the form 𝑥 2 + 2 𝑥 + 3 ( 𝑥 − 1 ) 2 ( 𝑥 − 2 ) ( 𝑥 2 + 4 ) ?单项选择题

A

𝑥 2 + 2 𝑥 + 3 ( 𝑥 − 1 ) 2 ( 𝑥 − 2 ) ( 𝑥 2 + 4 ) = 𝐴 𝑥 − 1 + 𝐵 𝑥 + 𝐶 ( 𝑥 − 1 ) 2 + 𝐷 𝑥 − 2 + 𝐸 𝑥 2 + 4

B

𝑥 2 + 2 𝑥 + 3 ( 𝑥 − 1 ) 2 ( 𝑥 − 2 ) ( 𝑥 2 + 4 ) = 𝐴 𝑥 − 1 + 𝐵 𝑥 ( 𝑥 − 1 ) 2 + 𝐶 𝑥 − 2 + 𝐷 𝑥 + 𝐸 𝑥 2 + 4

C

𝑥 2 + 2 𝑥 + 3 ( 𝑥 − 1 ) 2 ( 𝑥 − 2 ) ( 𝑥 2 + 4 ) = 𝐴 𝑥 − 1 + 𝐵 ( 𝑥 − 1 ) 2 + 𝐶 𝑥 − 2 + 𝐷 𝑥 𝑥 2 + 4

D

𝑥 2 + 2 𝑥 + 3 ( 𝑥 − 1 ) 2 ( 𝑥 − 2 ) ( 𝑥 2 + 4 ) = 𝐴 𝑥 − 1 + 𝐵 ( 𝑥 − 1 ) 2 + 𝐶 𝑥 − 2 + 𝐷 𝑥 + 𝐸 𝑥 2 + 4

E

𝑥 2 + 2 𝑥 + 3 ( 𝑥 − 1 ) 2 ( 𝑥 − 2 ) ( 𝑥 2 + 4 ) = 𝐴 𝑥 − 1 + 𝐵 ( 𝑥 − 1 ) 2 + 𝐶 𝑥 − 2 + 𝐷 𝑥 2 + 4

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