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anonymous

  • one year ago

(5x^3 -x^2+8x -55)/(x^4 +5x^3+11x^2) decompose into partial functions...please help?

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  1. dinamix
    • one year ago
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    (5x^3-x^2+8x-55)/x(x^3+5x^2+11x) @hailbug i help u bit

  2. anonymous
    • one year ago
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    would I only be factoring one x from the denominator or x^2?

  3. dinamix
    • one year ago
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    no thats only u have thing little dude

  4. anonymous
    • one year ago
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    what? sorry I'm confused

  5. anonymous
    • one year ago
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    @hailbug why do need to decompose into partial functions?

  6. anonymous
    • one year ago
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    its part of my summer calc homework. i've searched every tutorial for this but I literally can't find anything that closely resembles this. I was hoping someone would help me out

  7. dinamix
    • one year ago
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    @hailbug u have use Euclidean division thats only

  8. anonymous
    • one year ago
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    @hailbug do need solution or answer?

  9. anonymous
    • one year ago
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    @ASAAD123 solution

  10. anonymous
    • one year ago
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    you need to start by factoring the whole denominator. The common denominator is x², so it's \[\frac{ 5x^3-x^2+8x-55 }{ x^2(x^2+5x+11) }\] Both of those are quadratic so you can use\(\frac{ Ax+B }{ ax^2+bx+c }\) as a guess. \[\frac{ 5x^3-x^2+8x-55 }{ x^2(x^2+5x+11) }=\frac{ Ax+B }{ x^2 }+\frac{ Cx+D }{ x^2+5x+11 }\]

  11. dinamix
    • one year ago
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    @peachpi yes this is the anwer

  12. anonymous
    • one year ago
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    for a full table http://tutorial.math.lamar.edu/Classes/CalcII/PartialFractions.aspx

  13. anonymous
    • one year ago
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    It's not the answer, just a guess at the format. You still have to multiply, solve the system, etc to get the coefficients

  14. anonymous
    • one year ago
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    thank you so much that makes so much sense. I was trying to factor everything thinking that was the answer

  15. dinamix
    • one year ago
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    i want ask u qustion how did u know degree of Numerator is Ax+B and cx+D not only D or ax^2 +cx+d ? @peachpi

  16. freckles
    • one year ago
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    the numerator should be at least one degree less than the denominator @dinamix

  17. dinamix
    • one year ago
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    cuz i like your method but i use only (euclidean division ) i want learn other method @peachpi @freckles

  18. freckles
    • one year ago
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    So if the denominator is 2nd degree, then new numerator choice should be something like Ax+B since this will also include B since A can be zero still (which means the degree of the numerator will be either 0 or 1).

  19. dinamix
    • one year ago
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    @freckles ty so much

  20. anonymous
    • one year ago
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  21. anonymous
    • one year ago
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    @peachpi so I got the answer \[((3x - 5)/x^2)+ ((2x-11)/x^2 +5x +11) \] is this correct?

  22. anonymous
    • one year ago
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    oh haha @ASAAD123 didn't see that, sorry

  23. anonymous
    • one year ago
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    \[\frac{ -5 }{ x^2 }+\frac{ 3 }{ x }+\frac{ 2x-11 }{ x^2+5x+11 }\]

  24. anonymous
    • one year ago
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    @hailbug correct

  25. dinamix
    • one year ago
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    denominator is degree 4 not 5 @ASAAD123

  26. dinamix
    • one year ago
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    u make mistake

  27. anonymous
    • one year ago
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    @dinamix where is that mistake?

  28. anonymous
    • one year ago
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    yes that's correct @ASAAD123

  29. dinamix
    • one year ago
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    its ax+d/x^2 + bx+c/x^2+5x+11

  30. anonymous
    • one year ago
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    the denominator is still degree 4. You can split that first one up and then the denominator will reduce to x. |dw:1440868401732:dw|

  31. dinamix
    • one year ago
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    hmm ok

  32. anonymous
    • one year ago
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    basically, you need to look at the degree of the least common denominator, not the sum of the individual degrees

  33. dinamix
    • one year ago
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    ok i understand know , ty

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