Suppose that Q(x) (x a)(x b), where a b, and let P Q be a proper rational function so that (a) Show that (b) Use this result to find the partial fraction decomposition for P(x) 3x 2 and Q(x) x 2 4x 12 P(x) Q(x) A (x a) B (x b)...

a Clearing denominators gives us Setting x a then yields while setting x b yields therefore ...

Suppose that Q(x) = (x a)(x b), where a b, and let P/Q be

Question:

Suppose that Q(x) = (x − a)(x − b), where a ≠ b, and let P/Q be a proper rational function so that

P(x) Q(x) A (x-a) + B (x-b)

(a) Show that A = P(a) Q'(a) and B= P(b) Q' (b)

(b) Use this result to find the partial fraction decomposition for P(x) = 3x − 2 and Q(x) = x²− 4x − 12.

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Calculus

ISBN: 9781319055844

4th Edition

Authors: Jon Rogawski, Colin Adams, Robert Franzosa

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Question Posted: Dec 02, 2023 11:05 PM

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Suppose that Q(x) = (x a)(x b), where a b, and let P/Q be

Question:

P(x) Q(x) A (x-a) + B (x-b)

Step by Step Answer:

a Clearing denominators gives us Setting x a then yields while setting x b yields therefore ...View the full answer

Calculus

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