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Math Help - please help improper fraction into partial fraction

  1. #1
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    please help improper fraction into partial fraction

    resolve into partial fraction

    X^4/(x^2+1)(x^2 - 1)

    key ^-to a power eg X^4 is x to a power 4

    sorry for the way the question is phrased but i dont know how 2 put x to the power 4 or any integer in any other way ,please could someone demonstrate

    regards
    jovan
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  2. #2
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    Quote Originally Posted by joey1 View Post
    resolve into partial fraction

    X^4/(x^2+1)(x^2 - 1)

    key ^-to a power eg X^4 is x to a power 4

    sorry for the way the question is phrased but i dont know how 2 put x to the power 4 or any integer in any other way ,please could someone demonstrate

    regards
    jovan
    Hopefully, you know that x^2- 1= (x- 1)(x+ 1) while x^2+ 1 cannot be factored with real coefficients. You want to find numbers A, B, C, and D such that
    \frac{x^4}{(x^2+1)(x-1)(x+1)}= \frac{Ax+ B}{x^2+ 1}+ \frac{C}{x- 1}+ \frac{D}{x+ 1}

    Start by multiplying both sides of the equation by (x^2+ 1)(x- 1)(x+ 1) to get rid of the fractions. There are a number of ways to find A, B, C, and D now. The simplest is choosing 4 different values of x to get 4 equations.
    Last edited by HallsofIvy; February 24th 2010 at 02:07 AM.
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  3. #3
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    thanks hallsofivy
    thats a great help
    1 more question how did you type is there a tool that you used
    i would like to learn how to add the power to x instead of typing x^2,it becomes confusing to read sometimes

    regards
    jovan
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  4. #4
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    thanks hallsofivy
    thats a great help
    1 more question how did you type is there a tool that you used
    i would like to learn how to add the power to x instead of typing x^2,it becomes confusing to read sometimes

    regards
    jovan
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  5. #5
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    This board is enabled with "LaTex" a very powerful formula formatting language. You access it by typing html code [math ] (without the space) to begin and [/math ] (again without the space) to end and putting LaTex code in between. There is a LaTex tutorial at
    http://www.mathhelpforum.com/math-help/latex-help/

    You get x^2+ 1 simply by typing [math ]x^2+ 1[/math ] (again, without the spaces inside [ ]. If I didn't include those spaces you wouldn't see the code!)

    You can do really complicated things such as
    \int_{-\infty}^\infty e^{-x^2} dx= \frac{1}{\sqrt{2\pi}}

    with the code
    [math ]\int_{-\infty}^\infty e^{-x^2} dx= \frac{1}{\sqrt{2\pi}}[/math ]

    Most of the codes begin with "\". Be sure to distinguish between that and the "/" that ends the LaTex.

    "{" and "}" group entries. For example "e^-x^2" without the { } would give
    e^-x^2.

    Finally, you can see the code used for any formula by clicking on that formula.

    By the way, while this board uses a version that take [math ] and [/math ], other websites may use [Latex] [/Latex] or .
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  6. #6
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    Hello, joey1

    Resolve into partial fractions: . <br />
\frac{x^4}{(x^2+1)(x^2 - 1)}
    You already noted that the fraction is improper.

    It must be divided and then we will deal with the remainder.


    So we have: . \frac{x^4}{x^4-1} \:=\:1 + \frac{1}{x^4-1}


    And we work with the fraction:

    . . \frac{1}{(x-1)(x+1)(x^2+1)} \;=\;\frac{A}{x-1} + \frac{B}{x+1} + \frac{Cx+D}{x^2+1}


    We get: . A = \frac{1}{4},\;\; B = -\frac{1}{4},\;\; C= 0,\;\;  D = -\frac{1}{2}


    Answer: . 1 + \frac{\frac{1}{4}}{x-1} - \frac{\frac{1}{4}}{x+1} - \frac{\frac{1}{2}}{x^2+1}



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  7. #7
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    solve for THETA

    2tan^2theta +sec theta -4=0
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  8. #8
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    full working of problem

    thanx for this solution, but is there someplace I couold be able to see the full working of this problem, im really struggling.

    please help
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