Math 1508 Names
Group Work โ Week 4
Please show all work for credit. Good luck!
1. (5 points each) Write the form of the partial fraction decomposition of the rational
functions. The first few are done for you.
(a) 6
x3
โ9x2Note that we must first factor the denominator completely.
Answer: 6
x(xโ3)(x+ 3) =A
x+B
xโ3+C
x+ 3
(b) 4xโ9
(x2+ 5x+ 1)(x+ 3)2Here, the denominator is already factored completely.
Answer: Ax +B
x2+ 5x+ 1 +C
x+ 3 +D
(x+ 3)2
(c) 2x2
โ9
x3(x2+ 9)3(x4+ 5x+ 1) Here, the denominator is already factored completely.
Answer: A
x+B
x2+C
x3+Dx +E
x2+ 9 +F x +G
(x2+ 9)2+Hx +I
(x2+ 9)3+J x3+Kx2+Lx +M
x4+ 5x+ 1
(d) 1
9x2
โ1
