Sec 3: Partial Fractions - Edubirdie

University:
Stanford University
Course:
Introduction to Mathematical Thinking
Academic year:

2023
Views:

482

Pages:

2
Author:

MAlphen

Partial Fractions 1 Express 2 Express 3 3𝑥 +6𝑥−8 𝑥(𝑥2+2) in partial fractions. 2 𝑥 +2𝑥−19 as a sum of three partial fractions. (𝑥−1)(𝑥+3)2 Partial Fractions 1 Solution: By long division, 4 4𝑥 𝑥 (𝑥2+2) Answer: 3 − + [7] [5] 2 Solution: 𝑥2 + 2𝑥 − 19 𝐴 𝐵 𝐶 = + + (𝑥 − 1)(𝑥 + 3)2 (𝑥 − 1) 𝑥 + 3 (𝑥 + 3)2 𝑥2 + 2𝑥 − 19 = 𝐴(𝑥 + 3)2 + 𝐵(𝑥 − 1)(𝑥 + 3) + 𝐶(𝑥 − 1) Sub 𝑥 = 1, −16 = 16𝐴 𝐴 = −1 Sub 𝑥 = −3, −16 = −4𝐶 𝐶=4 Sub 𝑥 = 0, −19 = 9𝐴 − 3𝐵 − 𝐶 Sub 𝐴 = −1, 𝐶 = 4, −19 = −9 − 3𝐵 − 4 𝐵=2 𝑥2 + 2𝑥 − 19 1 2 4 = − + + (𝑥 − 1)(𝑥 + 3)2 (𝑥 − 1) (𝑥 + 3) (𝑥 + 3)2 Answer: − 1 2 4 + + (𝑥−1) 𝑥+3 (𝑥+3)2

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