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How to find the partial fractions for this expression?

  1. Jul 22, 2014 #1
    1. The problem statement, all variables and given/known data

    Find the partial fractions for this expression.

    (((n+1)*(sqrt(n)) - n*(sqrt(n+1))) / (n*(n+1)))

    3. The attempt at a solution

    The final answer is 1/sqrt(n) - 1/(sqrt(n+1))

    My work:

    A/n - B/(n+1) = n*sqrt(n+1) - (n+1)*(sqrt(n))
    I am subbing in n = -1 and n = 0 to solve for A and B which usually works but in this case it is giving me A = 0 and B = 0, which means I am getting 0 as my partial fraction. Thank you for your help.
  2. jcsd
  3. Jul 22, 2014 #2


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    Homework Helper

    Your expression doesn't require partial fractions, it requires re-writing as [tex]
    \frac{(n+1)\sqrt{n} - n\sqrt{n+1}}{n(n+1)} = \frac{(n+1)\sqrt{n}}{n(n+1)} -\frac{n\sqrt{n+1}}{n(n+1)}[/tex] and further simplifications in each term.
  4. Jul 22, 2014 #3
    Thank you very much !
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