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

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

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(5x^3-x^2+8x-55)/x(x^3+5x^2+11x) @hailbug i help u bit
would I only be factoring one x from the denominator or x^2?
no thats only u have thing little dude

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what? sorry I'm confused
@hailbug why do need to decompose into partial functions?
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
@hailbug u have use Euclidean division thats only
@hailbug do need solution or answer?
@ASAAD123 solution
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. \[\frac{ 5x^3-x^2+8x-55 }{ x^2(x^2+5x+11) }=\frac{ Ax+B }{ x^2 }+\frac{ Cx+D }{ x^2+5x+11 }\]
@peachpi yes this is the anwer
for a full table http://tutorial.math.lamar.edu/Classes/CalcII/PartialFractions.aspx
It's not the answer, just a guess at the format. You still have to multiply, solve the system, etc to get the coefficients
thank you so much that makes so much sense. I was trying to factor everything thinking that was the answer
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
the numerator should be at least one degree less than the denominator @dinamix
cuz i like your method but i use only (euclidean division ) i want learn other method @peachpi @freckles
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).
@freckles ty so much
@peachpi so I got the answer \[((3x - 5)/x^2)+ ((2x-11)/x^2 +5x +11) \] is this correct?
oh haha @ASAAD123 didn't see that, sorry
\[\frac{ -5 }{ x^2 }+\frac{ 3 }{ x }+\frac{ 2x-11 }{ x^2+5x+11 }\]
@hailbug correct
denominator is degree 4 not 5 @ASAAD123
u make mistake
@dinamix where is that mistake?
yes that's correct @ASAAD123
its ax+d/x^2 + bx+c/x^2+5x+11
the denominator is still degree 4. You can split that first one up and then the denominator will reduce to x. |dw:1440868401732:dw|
hmm ok
basically, you need to look at the degree of the least common denominator, not the sum of the individual degrees
ok i understand know , ty

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