Expert: Sherman D. - 5/26/2005

Question
write the rational expression as a sum of partial fractions.

1) x^2 + 8 / x^3 + 3x^2 + 2x

Answer
(x^2 + 8)/(x^3 + 3x^2 + 2x)
(x^2 + 8)/(x(x^2 + 3x + 2))

x^2 + 8 = A(x^2 + 3x + 2) + (Bx + C)x
x^2 + 8 = Ax^2 + 3Ax + 2A + Bx^2 + Cx
x^2 + 8 = (A + B)x^2 + (3A + C)x + 2A

this is the same as saying

x^2 + 0x + 8 = (A + B)x^2 + (3A + C)x + 2A

knowing this will help a lot

Now using just the coefficients

A + B = 1
3A + C = 0
2A = 8

2A = 8
A = 4

A + B = 1
4 + B = 1
B = -3

3A + C = 0
3(4) + C = 0
12 + C = 0
C = -12

so this gives you a Partial Fraction of

(4/x) - ((3x + 12)/(x^2 + 3x + 2))

so

((x^2+8)/(x^3+3x^2+2x)) = (4/x) - ((3x+12)/(x^2+3x+2))

Info found at http://tutorial.math.lamar.edu/AllBrowsers/1314/PartialFractions.asp