1. dinamix

(5x^3-x^2+8x-55)/x(x^3+5x^2+11x) @hailbug i help u bit

2. anonymous

would I only be factoring one x from the denominator or x^2?

3. dinamix

no thats only u have thing little dude

4. anonymous

what? sorry I'm confused

5. anonymous

@hailbug why do need to decompose into partial functions?

6. anonymous

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

@hailbug u have use Euclidean division thats only

8. anonymous

@hailbug do need solution or answer?

9. anonymous

10. anonymous

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

@peachpi yes this is the anwer

12. anonymous
13. anonymous

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

thank you so much that makes so much sense. I was trying to factor everything thinking that was the answer

15. dinamix

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

the numerator should be at least one degree less than the denominator @dinamix

17. dinamix

cuz i like your method but i use only (euclidean division ) i want learn other method @peachpi @freckles

18. 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).

19. dinamix

@freckles ty so much

20. anonymous

21. anonymous

@peachpi so I got the answer $((3x - 5)/x^2)+ ((2x-11)/x^2 +5x +11)$ is this correct?

22. anonymous

oh haha @ASAAD123 didn't see that, sorry

23. anonymous

$\frac{ -5 }{ x^2 }+\frac{ 3 }{ x }+\frac{ 2x-11 }{ x^2+5x+11 }$

24. anonymous

@hailbug correct

25. dinamix

denominator is degree 4 not 5 @ASAAD123

26. dinamix

u make mistake

27. anonymous

@dinamix where is that mistake?

28. anonymous

29. dinamix

its ax+d/x^2 + bx+c/x^2+5x+11

30. anonymous

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

hmm ok

32. anonymous

basically, you need to look at the degree of the least common denominator, not the sum of the individual degrees

33. dinamix

ok i understand know , ty