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Homework Help: Differential Calculus - Question

  1. Oct 17, 2011 #1
    1. The problem statement, all variables and given/known data

    I don't understand how this can be written like this:

    [tex]\frac{1}{(2x+1)^{1/2}}-\frac{1}{(2x+1)^{3/2}}=\frac{2x+1-1}{(2x+1)^{3/2}}=\frac{2x}{(2x+1)^{3/2}}[/tex]


    What's the rule which makes this possible and explain please.
     
  2. jcsd
  3. Oct 17, 2011 #2

    HallsofIvy

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    Science Advisor

    The "rule" is one that you probably learned in the third grade: you add or subtract fractions by getting a "common denominator".

    The first fraction has denominator [itex](2x+1)^{1/2}[/itex]. The second fraction has denominator [itex](2x+ 1)^{3/2}= (2x+1)^{1+ 1/2}= (2x+1)(2x+1)^{1/2}[/itex].

    In other words, the common denominator is [itex](2x+1)^{3/2}[/itex] and you get it by multiplying the numerator and denominator of the first fraction by 2x+1.
     
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