Math 1508 Name
Quiz #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) 5x+ 3
x3(x2+ 6)2Do not solve for the constants.
