SOLUTION: Express in partial frations {{{(x^3+2x^2-10x-9)/(x^2-9)}}}

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Express in partial frations {{{(x^3+2x^2-10x-9)/(x^2-9)}}}      Log On


   

Question 1072991: Express in partial frations %28x%5E3%2B2x%5E2-10x-9%29%2F%28x%5E2-9%29
Found 2 solutions by josgarithmetic, youngguru23:
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
Try polynomial division, and then decompose the remainder if any.

QUOTIENT is x%2B2
REMAINDER is -%28x%2B9%29

Your original rational expression is x%2B2-%28x%2B9%29%2F%28x%5E2-9%29.
Now, can you decompose that rational expression remainder on your own, or still need help?


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Finished result, highlight%28x%2B2%2B%28-2%29%2F%28x-3%29%2B2%2F%28x%2B3%29%29


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FURTHER HELP---------
Starting from x%2B2%2B%28-x-9%29%2F%28x%5E2-9%29

Split the remainder expression into sum of two fractions.

%28-x-9%29%2F%28%28x-3%29%28x%2B3%29%29=A%2F%28x-3%29%2BB%2F%28x%2B3%29

Multiply both sides by the simplest common denominator

-x-9=A%28x%2B3%29%2BB%28x-3%29
-x-9=Ax%2B3A%2BBx-3B
-x-9=%28A%2BB%29x%2B3%28A-B%29
Equate coefficients or factors according to corresponding positions.

system%28A%2BB=-1%2C3%28A-B%29=-9%29
And solving this system, you should find system%28A=-2%2Cand%2CB=2%29.

Answer by youngguru23(3) About Me  (Show Source):
You can put this solution on YOUR website!
I still need more help