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

College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter5: Systems Of Equations And Inequalities
Section5.3: Partial Fractions
Problem 4E
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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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