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Math Help - Partial fraction again

  1. #1
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    Post Partial fraction again

    I got this problem out the multiple choice section in my math book.
    It said if \frac {x+p}{(x-1)(x-3)}\equiv \frac {q}{x-1}+\frac{2}{x-3} what are the values of p and q?
    Then I got another one that seem to be quite similar if x^2+4x+p \equiv (x+q)^2+1 what are the value of p and q? Trying to find two values is what that is confusing to me...
    Can some one please help me with these problem?
    Last edited by scrible; October 24th 2009 at 03:20 PM.
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  2. #2
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    The first problem has one equation with 2 variables.

    For the second it seems like you should equate coefficents but the information seems to be scarce. Is there any other bits and pieces you can reveal?
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  3. #3
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    Post Partial fraction again

    sorry I don't have any other information except that.
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  4. #4
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    Quote Originally Posted by scrible View Post
    I got this problem out the multiple choice section in my math book.
    It said if \frac {x+p}{(x-1)(x-3)}\equiv \frac {q}{x-1}+\frac{2}{x-3} what are the values of p and q?
    x+p = q(x-3) + 2(x-1)

    let x = 1 ...

    1+p = -2q

    let x = 3 ...

    3+p = 4

    p = 1 , q = -1
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  5. #5
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    Quote Originally Posted by skeeter View Post
    x+p = q(x-3) + 2(x-1)

    let x = 1 ...

    1+p = -2q

    let x = 3 ...

    3+p = 4

    p = 1 , q = -1


    Thank you very much, but can you please help me with this one also? if x^2+4x+p \equiv (x+q)^2+1 what are the value of p and q? Trying to find two values is what that is confusing to me...
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  6. #6
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    Quote Originally Posted by scrible View Post
    Thank you very much, but can you please help me with this one also? if x^2+4x+p \equiv (x+q)^2+1 what are the value of p and q? Trying to find two values is what that is confusing to me...
    Several approaches are possible, including the following:

    x^2 + 4x + p \equiv x^2 + 2qx + q^2 + 1.

    Compare coefficients on each side:

    4 = 2q .... (1)

    p = q^2 + 1 .... (2)

    Solve equations (1) and (2) simultaneously.
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