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Partial fractions division question

Hi I realise (x^2 -1) is difference of two squares but I couldn’t get an answer doing the division or by multiplying by (x^2 -1)
image.jpg523.2KB
Think about what the denominators will be. You're right about the difference of two squares, so what would they be when expanded?

This might help some more:

Spoiler





Let me know if this clears things up!
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Spoiler


Thanks, I would have done that if it wasn’t for the x^2 + B part. Should I multiply by through the factorised brackets and compare coefficients?
Original post by e1eanor

Spoiler


Thanks, I would have done that if it wasn’t for the x^2 + B part. Should I multiply by through the factorised brackets and compare coefficients?

Yep! That should get you to the right answer
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Original post by Purple43Monkey
Yep! That should get you to the right answer

x^4 +2 = (x+1)(x-1)x^2 + B(x+1)(x-1) + C(x+1)(x-1)?
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Original post by e1eanor
x^4 +2 = (x+1)(x-1)x^2 + B(x+1)(x-1) + C(x+1)(x-1)?

Wait ignore the brackets on the C and I got C=3 and B=1
Sorry, in this case you substitute, so let x=1 and then let x=-1
I think it should only split into 2 terms

maths 2.jpg

Does this work and make sense?
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Original post by Purple43Monkey
Sorry, in this case you substitute, so let x=1 and then let x=-1

Got it, can I ask about a two-marker on the same topic?
Of course!
Original post by Purple43Monkey
I think it should only split into 2 terms



Does this work and make sense?


Don't post solutions - sorry, it looks wrong anyway
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image.jpgQuestion 5 part b - for part a I got it equals 1+ 2/x+1 + 3/2x-1
Ah yeah im so sorry, for the first question you need to firstly divide as you have a top heavy fraction, then you do that step. Basically you did the first step right, then you do the extra bit. I can pm you the answer if you want
(edited 1 year ago)
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Original post by Purple43Monkey
Ah yeah im so sorry, for the first question you need to firstly divide as you have a top heavy fraction, then you do that step. Basically you did the first step right, then you do the extra bit. I can pm you the answer if you want

Do I just sub in x=1/2? It’s the inequality it wants that’s confusing me. Should be obvious
Original post by e1eanor
Do I just sub in x=1/2? It’s the inequality it wants that’s confusing me. Should be obvious


Sorry i meant for your original question you need to first do polynomial division (as I think you originally did) and then split into partial fractions. I appear to be a bit brain dead at the moment. Apologies for any confusion!
(edited 1 year ago)
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Original post by Purple43Monkey
Sorry i meant for your original question you need to first do polynomial division (as I think you originally did) and then split into partial fractions. I appear to be a bit brain dead at the moment. Apologies for any confusion!


I’ve got the answer for part a, it’s part b :smile:
Original post by e1eanor
I’ve got the answer for part a, it’s part b :smile:


Just think about the signs of the different partial fractions when x>1/2
(edited 1 year ago)

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