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Practice the technique with the following expressions: 4s-1 (iv) s2 +14s-32

Practice the technique with the following expressions: 4s-1 (iv) s2 +14s-32

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Practice the technique with the following expressions: 4s-1 (iv) s2 +14s-32 2s+3 (v) (s-1)2 4s2 -5s+6 (vi) (s+1)(s²+4)
Transcribed Image Text:Practice the technique with the following expressions: 4s-1 (iv) s2 +14s-32 2s+3 (v) (s-1)2 4s2 -5s+6 (vi) (s+1)(s²+4)
Part 2 Partial Fractions Зх-4 Express as a sum of partial fractions x2-5x+6 3x – 4 Зх — 4 A B х2 — 5х + 6 (х — 3)(х — 2) X – 3 х — 2 Multiplying each term by (x-3)(x-2) results in: 3x – 4 = A(x – 2) + B(x – 3) Let x = 2: 3(2) – 4 = A(2 – 2) + B(2 – 3) 2 = A(0) + B(-1) Therefore, B = -2 Let x = 3: 3(3) — 4 %3D А(3 - 2) + B(3 — 3) 5 = A(1) + B(0) Therefore, A = 5 So Зх — 4 5 2 (x – 3)(x – 2) X - 3 X – 2 +
Transcribed Image Text:Part 2 Partial Fractions Зх-4 Express as a sum of partial fractions x2-5x+6 3x – 4 Зх — 4 A B х2 — 5х + 6 (х — 3)(х — 2) X – 3 х — 2 Multiplying each term by (x-3)(x-2) results in: 3x – 4 = A(x – 2) + B(x – 3) Let x = 2: 3(2) – 4 = A(2 – 2) + B(2 – 3) 2 = A(0) + B(-1) Therefore, B = -2 Let x = 3: 3(3) — 4 %3D А(3 - 2) + B(3 — 3) 5 = A(1) + B(0) Therefore, A = 5 So Зх — 4 5 2 (x – 3)(x – 2) X - 3 X – 2 +
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