Practice the technique with the following expressions: 4s-1 (iv) s2 +14s-32
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter2: Equations And Inequalities
Section2.1: Equations
Problem 54E
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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)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffb6ef112-0fda-41dc-bad6-913ca56d167c%2Ff38a4ed9-b0e9-45b7-8cd1-eb7320862b01%2Fabarmt_processed.png&w=3840&q=75)
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
+](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffb6ef112-0fda-41dc-bad6-913ca56d167c%2Ff38a4ed9-b0e9-45b7-8cd1-eb7320862b01%2Fnekpwvg_processed.png&w=3840&q=75)
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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