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Math Help - Partial Fractions

  1. #1
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    Red face Partial Fractions

    Hi everyone!

    The problem I need help with is:

    Preform partial fraction decomposition: x / 4x2 + 4x + 1

    In the solution to this exercise the author first factorizes the denominator, which factorizes into (2x + 1)2, but than he writes that

    x / (2x + 1)2 = A / (2x + 1) + B / (2x + 1)2, I am unsure why this is the case? I understand that it can't be A / (2x + 1) + B / (2x + 1) either, but the authors approach seems wrong to me (don't worry I know I am wrong, hehe), because (2x + 1)2 is the original factorization of 4x2 + 4x + 1, so adding (2x + 1) to it, would in my eyes give a bigger number than 4x2 + 4x + 1 .

    Also, my teacher in Calculus 1 at university said that for the exam it is most important that we learn how to draw graphs and than the rest will come on its own. I assume that was meant as a joke, but he never jokes, so now I am trying to read into his statement to see if there is a underlying hidden message in it.

    Thanks to anyone for reading this and helping out
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  2. #2
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    Re: Partial Fractions

    Quote Originally Posted by Nora314 View Post
    Preform partial fraction decomposition: x / 4x2 + 4x + 1

    x / (2x + 1)2 = A / (2x + 1) + B / (2x + 1)2, I am unsure why this is the case? I understand that it can't be A / (2x + 1) + B / (2x + 1) either, but the authors approach seems wrong to me (don't worry I know I am wrong, hehe), because (2x + 1)2 is the original factorization of 4x2 + 4x + 1, so adding (2x + 1) to it, would in my eyes give a bigger number than 4x2 + 4x + 1 .

    When we add \frac{x}{(x-2)}+\frac{x+1}{(x-2)^2} what is the LCD?

    If you see that correctly then you answer your own question.
    Thanks from Nora314
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  3. #3
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    Re: Partial Fractions

    Thank you so much, , I understand now!
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