SOLUTION: decompose into a partial fraction 2x^3+x^2-3x+5 / x^2-2x-3

Question 117478: decompose into a partial fraction
2x^3+x^2-3x+5 / x^2-2x-3
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Decompose into a partial fraction
:

:
Numerator degree is greater than the denominator:
Divide using long division:
......................___________________
(x^2-2x-3)|2x^3 + x^2 - 3x+ 5
:
You should get 2x + 5: + Remainder
:
Decompose the remainder:

Factor the denominator
= + =
:
Since these fractions have the same denominator, their numerators have to be equal
13x+20 = A(x+1) + B(x-3)
:
Let x = 3, then B drops out and we can solve for A:
13(3) + 20 = A(3+1) + B(3-3)
:
39 + 20= A(4) + B(0)
:
59 = 4A
:
A = 59/4
:
A = 14.75
:
Let x = -1, then A drops out
13(-1) + 20 = A(-1+1) + B(-1-3)
:
-13 + 20 = A(0) + B(-4)
:
7 = -4B
:
B = 7/-4
:
B = -1.75
:
The quotient and the partial fractions:
(2x + 5) + +

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