SOLUTION: How can I express the following expression in partial fractions: 9x^2 - 22x + 9 / x^3 - 4x^2 + 3x Help me ASAP. Thanks in advance.

Question 669506: How can I express the following expression in partial fractions:
9x^2 - 22x + 9 / x^3 - 4x^2 + 3x
Help me ASAP.
Thanks in advance.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
express the following expression in partial fractions:
9x^2 - 22x + 9 / x^3 - 4x^2 + 3x
----
x^3 - 4x^2 + 3x = x(x^2-4x+3)
------
Rewrite:
9x^2-22x+9 /x^3 -4x^2+3x = a/x + bx+c/(x^2-4x+3)
----
9x^2-22x+9 = a(x^2-4x+3) + (bx+c)x
----
9x^2-22x+9 = ax^2 -4ax + 3a + bx^2 + cx
----
9x^2 - 22x + 9 = (a+b)x^2 +(-4a+c)x + 3a
-----
Equate the coefficients of Like terms to get:
Equations:
a+b = 9
-4a+c = -22
3a = 9
-----
Solve for a, b, c:
a = 3
b = 9-a = 6
c = -22+4a = -10
----
Partial-Fraction Form
Fraction = 3/x + (6x-10)/(x^2-4x+3)
====================
Cheers,
Stan H.

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