Partial fractions division question

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e1eanor
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#1
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#1
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)
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Purple43Monkey
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#2
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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:

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Let me know if this clears things up!
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e1eanor
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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?
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Purple43Monkey
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(Original post by e1eanor)
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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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e1eanor
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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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e1eanor
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#6
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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
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Purple43Monkey
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Sorry, in this case you substitute, so let x=1 and then let x=-1
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Purple43Monkey
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#8
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I think it should only split into 2 terms

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Does this work and make sense?
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e1eanor
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#9
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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?
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Purple43Monkey
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Of course!
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Muttley79
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#11
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(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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e1eanor
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Name:  image.jpg
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Size:  125.3 KBQuestion 5 part b - for part a I got it equals 1+ 2/x+1 + 3/2x-1
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Purple43Monkey
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#13
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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
Last edited by Purple43Monkey; 1 month ago
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e1eanor
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#14
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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
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Purple43Monkey
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(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!
Last edited by Purple43Monkey; 1 month ago
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e1eanor
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#16
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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
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mqb2766
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#17
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(Original post by e1eanor)
I’ve got the answer for part a, it’s part b
Just think about the signs of the different partial fractions when x>1/2
Last edited by mqb2766; 1 month ago
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