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anonymous

  • 4 years ago

Expand the expression in powers of x to x^3 1 -4 ---- - ----- 2x+1 4+x^2

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  1. anonymous
    • 4 years ago
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    Sorry, it's mean to be 4 and not -4

  2. anonymous
    • 4 years ago
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    I think... \[(x^2-8)/(2x^3+x^2+8x+4)\]

  3. anonymous
    • 4 years ago
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    ahh, shoot, (x^2-8x), sry

  4. anonymous
    • 4 years ago
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    Um no... it's expansion... not simplifying...

  5. ash2326
    • 4 years ago
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    \(1/ (2x+1)-4/(4+x^2)\) \((4+x^2-8x-4)/( 2x^3+x^2+8x+4)\) \((x^2-8x)/( 2x^3+x^2+8x+4)\)

  6. anonymous
    • 4 years ago
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    i think you have to do this piece by piece, using \[\frac{1}{1-r}=1+r+r^2+r^3 + ...\] or in this case \[\frac{1}{1+x}=1-x+x^2-x^3+...\]

  7. anonymous
    • 4 years ago
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    How do you do it that way, satellite?

  8. ash2326
    • 4 years ago
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    order which grade question is this??

  9. anonymous
    • 4 years ago
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    It's last year of highschool... so, pretty high (Uni first year)

  10. ash2326
    • 4 years ago
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    then we'll have to use satellite's method

  11. anonymous
    • 4 years ago
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    ok that was wrong, it is just the way you want it. \[\frac{1}{1+2x}=1-(2x)+(2x)^2-(2x)^3+...\] but we can stop there because you only need first four terms

  12. anonymous
    • 4 years ago
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    \[\frac{4}{4+x^2}\] is more of a pain because you have to have a one in the denominator, so divide top and bottom by 4 to get \[\frac{1}{1+\frac{x^2}{4}}\] and repeat the process

  13. anonymous
    • 4 years ago
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    with judicious use of parentheses you get \[\frac{1}{1+\frac{x^2}{4}}=1-(\frac{x^2}{4})+(\frac{x^2}{4})^2\] but really we can stop here because you only need up to \[x^3\] for your problem

  14. anonymous
    • 4 years ago
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    your last job is to combine like terms for \[1-2x+4x^2-8x^3-\left(1-\frac{x^2}{4}\right )\]

  15. anonymous
    • 4 years ago
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    Thanks!

  16. anonymous
    • 4 years ago
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    yw

  17. anonymous
    • 4 years ago
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    oh look, we can even check that it is right, by looking at the first 3 terms here http://www.wolframalpha.com/input/?i=1%2F%282x%2B1%29-4%2F%284%2Bx^2%29

  18. anonymous
    • 4 years ago
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    It is right :) I know how you got it now. Thank you

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