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Question 1 of 5Find the partial fraction decomposition of each:
$$\frac{4x^2 + 16 - 6x}{x^3 + x - 2x^2 - 2}$$
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Select the Correct Answer Below: Correct! Cool Emoji Not Correct! Cool Emoji
A
$$\frac{-1}{x - 2}- \frac{1}{x^2 + 1}$$
B
$$\frac{6}{x - 2}- \frac{3}{x^2 + 1}$$
C
$$\frac{2}{x - 2}- \frac{4}{x^2 + 1}$$
D
$$\frac{1}{x - 2}- \frac{3}{x^2 + 1}$$
E
$$\frac{4}{x - 2}- \frac{6}{x^2 + 1}$$
Question 2 of 5Find the partial fraction decomposition of each:
$$\frac{-4x^3 - 26x + 17x^2 + 75}{x^4 + 5x^2 - 3x^3 - 15x}$$
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Select the Correct Answer Below: Correct! Cool Emoji Not Correct! Cool Emoji
A
$$\frac{-5}{x}+ \frac{2}{x - 3}- \frac{2}{x^2 + 5}$$
B
$$\frac{4}{x}- \frac{6}{x - 3}+ \frac{4}{x^2 + 5}$$
C
$$\frac{-5}{x}+ \frac{1}{x - 3}+ \frac{2}{x^2 + 5}$$
D
$$\frac{3}{x}+ \frac{1}{x - 3}+ \frac{4}{x^2 + 5}$$
E
$$\frac{-7}{x}+ \frac{1}{x - 3}+ \frac{9}{x^2 + 5}$$
Question 3 of 5Find the partial fraction decomposition of each:
$$\frac{-2x^3 + 8 + 4x^2}{x^3 + 2x}$$
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Select the Correct Answer Below: Correct! Cool Emoji Not Correct! Cool Emoji
A
$$-2 + \frac{4}{x}+ \frac{4}{x^2 + 2}$$
B
$$-2 + \frac{3}{x}- \frac{6}{x^2 + 2}$$
C
$$-2 + \frac{5}{x}- \frac{3}{x^2 + 2}$$
D
$$-2 - \frac{1}{x}- \frac{3}{x^2 + 2}$$
E
$$-2 + \frac{1}{3x}- \frac{2}{5(x^2 + 2)}$$
Question 4 of 5Find the partial fraction decomposition of each:
$$\frac{2x^4 + 34x^2 + 126 + 7x^3 + 38x}{(x + 2)(x^2 + 5)^2}$$
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Select the Correct Answer Below: Correct! Cool Emoji Not Correct! Cool Emoji
A
$$\frac{-4}{x + 2}- \frac{2}{x^2 + 5}- \frac{2}{(x^2 + 5)^2}$$
B
$$\frac{-3}{x + 2}- \frac{7}{x^2 + 5}- \frac{6}{(x^2 + 5)^2}$$
C
$$\frac{4}{x + 2}- \frac{7}{x^2 + 5}- \frac{2}{(x^2 + 5)^2}$$
D
$$\frac{2}{x + 2}+ \frac{7}{x^2 + 5}+ \frac{3}{(x^2 + 5)^2}$$
E
$$\frac{-1}{x + 2}+ \frac{-2}{7(x^2 + 5)}- \frac{3}{(x^2 + 5)^2}$$
Question 5 of 5Find the partial fraction decomposition of each:
$$\frac{-6x^2 + 13}{(x^2 - 2)^2}$$
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Select the Correct Answer Below: Correct! Cool Emoji Not Correct! Cool Emoji
A
$$\frac{3}{x^2 - 2}- \frac{6}{(x^2 - 2)^2}$$
B
$$\frac{-6}{x^2 - 2}+ \frac{1}{(x^2 - 2)^2}$$
C
$$\frac{-6}{5(x^2 - 2)}+ \frac{1}{(x^2 - 2)^2}$$
D
$$\frac{-6}{x^2 - 2}+ \frac{9}{(x^2 - 2)^2}$$
E
$$\frac{-5}{x^2 - 2}+ \frac{8}{(x^2 - 2)^2}$$

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