SOLUTION: express as partial fractions - 3x^3-x^2-13x-13 / x^2-x-6

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Question 950724: express as partial fractions -
3x^3-x^2-13x-13 / x^2-x-6
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Dividing first,
%283x%5E3-x%5E2-13x-13%29+%2F+%28x%5E2-x-6%29=%283x%2B2%29%2B%287x-1%29%2F%28x%5E2-x-6%29
So then,
%287x-1%29%2F%28%28x-3%29%28x%2B2%29%29=A%2F%28x-3%29%2BB%2F%28x%2B2%29
7x-1=A%28x%2B2%29%2BB%28x-3%29
7x-1=%28A%2BB%29x%2B%282A-3B%29
which leads to,
A%2BB=7
2A-3B=-1
Multiply the first by 2 and subtract from the second to eliminate A,
2A-3B-2A-2B=-1-14
-5B=-15
B=3
Then,
A%2B3=7
A=4
So finally,
%283x%5E3-x%5E2-13x-13%29+%2F+%28x%5E2-x-6%29=%283x%2B2%29%2B4%2F%28x-3%29%2B3%2F%28x%2B2%29