1. Match the rational functions (a)-(d) with the corresponding partial fraction decompositions (i)–(iv). x² + 4x + 12 (a) (x + 2)(x² + 4) 2x2 + 8x + 24 (b) (x + 2)2(x² +4) x2 – 4x + 8 (c) (x – 1)2(x – 2)2 x4 – 4x + 8 (d) (x +2)(x² + 4) 4 (i) х — 2+ 4х — 4 X +2 x² +4 -8 (ii) (x – 2)2 (х — 1)2 х -x +2 x2 +4 4 (iii) (x + 2)2 (iv) x+2 x2 +4

College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter6: Linear Systems
Section6.6: Partial Fractions
Problem 59E
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1. Match the rational functions (a)-(d) with the corresponding partial fraction decompositions (i)–(iv).
x² + 4x + 12
(a)
(x + 2)(x² + 4)
2x2 + 8x + 24
(b)
(x + 2)2(x² +4)
x2 – 4x + 8
(c)
(x – 1)2(x – 2)2
x4 – 4x + 8
(d)
(x +2)(x² + 4)
4
(i) х — 2+
4х — 4
X +2
x² +4
-8
(ii)
(x – 2)2
(х — 1)2
х
-x +2
x2 +4
4
(iii)
(x + 2)2
(iv)
x+2
x2 +4
Transcribed Image Text:1. Match the rational functions (a)-(d) with the corresponding partial fraction decompositions (i)–(iv). x² + 4x + 12 (a) (x + 2)(x² + 4) 2x2 + 8x + 24 (b) (x + 2)2(x² +4) x2 – 4x + 8 (c) (x – 1)2(x – 2)2 x4 – 4x + 8 (d) (x +2)(x² + 4) 4 (i) х — 2+ 4х — 4 X +2 x² +4 -8 (ii) (x – 2)2 (х — 1)2 х -x +2 x2 +4 4 (iii) (x + 2)2 (iv) x+2 x2 +4
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