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Another Partial Fractions question

Hello there!

I arrived at an answer for this question. But it isn't the correct answer, as per my solutions sheet (or is it an equivalent? Ive tried checking and I don't think it is an equivalent answer).



Here are my workings:




However, the answer given is:


I would be very grateful if you could let me know where have I gone wrong.

Thank you!
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Reply 1
Avatar for TeeEm
TeeEm
19
Original post by Sidhant Shivram
Hello there!

I arrived at an answer for this question. But it isn't the correct answer, as per my solutions sheet (or is it an equivalent? Ive tried checking and I don't think it is an equivalent answer).



Here are my workings:




However, the answer given is:


I would be very grateful if you could let me know where have I gone wrong.

Thank you!


divide as fractions are improper

x3-1=(x-1)(x2+x+1) of which the quadratic factor is irreducible

A/x +B/x2 + C/(x-1) + (Dx+E)/(x2+x+1)

have fun!
Original post by TeeEm
divide as fractions are improper

x3-1=(x-1)(x2+x+1) of which the quadratic factor is irreducible

A/x +B/x2 + C/(x-1) + (Dx+E)/(x2+x+1)

have fun!



It should be x3+1=(x+1)(x2-x+1)


= A/x +B/x2 + C/(x+1) + (Dx+E)/(x2-x+1)



TS you are missing the C/(x+1) component in your expression.


Hope this helps.Peace.
(edited 9 years ago)
Reply 3
Avatar for TeeEm
TeeEm
19
Original post by WhiteGroupMaths
It should be x3+1=(x+1)(x2-x+1)


= A/x +B/x2 + C/(x+1) + (Dx+E)/(x2-x+1)



TS you are missing the C/(x+1) component in your expression.


Hope this helps.Peace.


Definitely does not help me as this this is not my problem...
anybody with half a molecule of brain can see the obvious typo.
Original post by TeeEm
divide as fractions are improper

x3-1=(x-1)(x2+x+1) of which the quadratic factor is irreducible

A/x +B/x2 + C/(x-1) + (Dx+E)/(x2+x+1)

have fun!


Original post by WhiteGroupMaths
It should be x3+1=(x+1)(x2-x+1)


= A/x +B/x2 + C/(x+1) + (Dx+E)/(x2-x+1)



TS you are missing the C/(x+1) component in your expression.


Hope this helps.Peace.


Thank you! It did help.
But just to confirm, I would still have to factorise the numerator as I did above (in my workings) since it is an improper fraction, right? Is there any other, more scientific means to do this rather than simply guessing what could be the right terms to put into the expression (the numerator) to factorise it so that it becomes proper?
Reply 5
Avatar for TeeEm
TeeEm
19
Original post by Sidhant Shivram
Thank you! It did help.
But just to confirm, I would still have to factorise the numerator as I did above (in my workings) since it is an improper fraction, right? Is there any other, more scientific means to do this rather than simply guessing what could be the right terms to put into the expression (the numerator) to factorise it so that it becomes proper?


this is just partial fractions so nothing scientific

If you do not like expanding to carry out the division then you should be able to see that


.... =1+ A/x +B/x2 + C/(x+1) + (Dx+E)/(x2-x+1)

since (x^5+ ....)/(x^5+...) can produce at most 1
Original post by TeeEm
this is just partial fractions so nothing scientific

If you do not like expanding to carry out the division then you should be able to see that


.... =1+ A/x +B/x2 + C/(x+1) + (Dx+E)/(x2-x+1)

since (x^5+ ....)/(x^5+...) can produce at most 1


Ahh, alright. Makes sense. Thanks again! You're a lifesaver!
Reply 7
Avatar for TeeEm
TeeEm
19
Original post by Sidhant Shivram
Ahh, alright. Makes sense. Thanks again! You're a lifesaver!


... no "lifesaver" but it was my pleasure
Original post by TeeEm
Definitely does not help me as this this is not my problem...
anybody with half a molecule of brain can see the obvious typo.


Try half a serving of humility a day for starters. Helps a lot for the arrogant soul.

Peace.
Reply 9
Avatar for TeeEm
TeeEm
19
Original post by WhiteGroupMaths
Try half a serving of humility a day for starters. Helps a lot for the arrogant soul.

Peace.


have a good day ...

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