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katieb

  • 5 years ago

What is the partial fraction decomposition? Please help me. These are impossible. :( -5x-15/(x+5)^2

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  1. anonymous
    • 5 years ago
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    You have a repeated linear factor in the denominator, so you decompose the fraction as such:\[\frac{-5x-15}{(x+5)^2}=\frac{A}{x+5}+\frac{B}{(x+5)^2}\]You then multiply both sides by (x+5)^2 to obtain\[-5x-15=A(x+5)+B\]Expand and collect like terms:\[-5x-15=Ax+(5A+B)\]In order for this to be true, we must have\[A=-5\](identifying it with the coefficient of x on the left) and \[5A+B=-15\]Since A has to be -5, we may solve for B:\[-15=5A+B=5(-5)+B=-25+B \rightarrow B=-15+25=10\]So A = -5 and B = 10, and your decomposition is\[\frac{-5x-15}{(x+5)^2}=-\frac{5}{x+5}+\frac{10}{(x+5)^2}\]

  2. anonymous
    • 5 years ago
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    You can always check by cross-multiplying the right-hand side to see if it gets you back to what you had originally.

  3. KatieB
    • 5 years ago
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    it's saying that's incorrect. :(

  4. anonymous
    • 5 years ago
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    Sorry, Katie, but the answer is correct. I've double-checked. Maybe you've entered something wrong?

  5. KatieB
    • 5 years ago
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    Ok, you're a genius. I forgot the negative. Please help me with 2 more problems?

  6. KatieB
    • 5 years ago
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    Done.

  7. KatieB
    • 5 years ago
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    partial decomposition of... x^3+x^2-5/(x^2+7)^2

  8. anonymous
    • 5 years ago
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  9. KatieB
    • 5 years ago
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    What is the partial fraction decomposition? 8x^2+20x+77/x(x-9)(x-8)

  10. KatieB
    • 5 years ago
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    Last one please and thank you so much, but it's due in 8 minutes.

  11. anonymous
    • 5 years ago
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    I can give you what I got, but I've rushed and can't guarantee. \[\frac{77/72}{x}+\frac{60535/616}{x-9}-\frac{63299/693}{x-8}\]

  12. anonymous
    • 5 years ago
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    wait

  13. anonymous
    • 5 years ago
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    -749/8 for the x-8 one 905/9 for x-9 one 77/72 for x one

  14. KatieB
    • 5 years ago
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    aw man too late

  15. KatieB
    • 5 years ago
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    thank you so much for trying! you're awesome!

  16. anonymous
    • 5 years ago
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    oh well...next time, don't leave it to the last minute! :p

  17. anonymous
    • 5 years ago
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    Go to khanacademy.org or YouTube if you need to see how partial fraction decomposition is done :)

  18. KatieB
    • 5 years ago
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    thank you!

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