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Relatively easy simplification

  1. Oct 7, 2008 #1

    thrill3rnit3

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    1. The problem statement, all variables and given/known data

    Simplify

    2. Relevant equations


    [tex]\frac{\sqrt{a-\sqrt{a}}\times\sqrt{a+\sqrt{a}}}{\sqrt{a-1}}[/tex]


    3. The attempt at a solution

    [tex]\frac{\sqrt{(a-\sqrt{a})(a+\sqrt{a})}}{\sqrt{a-1}}[/tex]

    [tex]\frac{\sqrt{a^2-a}}{\sqrt{a-1}} \times \frac{\sqrt{a-1}}{\sqrt{a-1}}[/tex]

    [tex]\frac{\sqrt{(a^2-a)(a-1)}}{a-1}[/tex]

    I'm not sure how to go from there, or if I did something wrong along the way. I just need that next step. thanks.
     
  2. jcsd
  3. Oct 7, 2008 #2

    Redbelly98

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    Can you factor (a2-a) ?
     
  4. Oct 7, 2008 #3

    thrill3rnit3

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    well if I factor [tex](a^2-a)[/tex], the numerator will just go back to the original expression times [tex](a-1)[/tex], right?
     
  5. Oct 7, 2008 #4

    rock.freak667

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    From here:

    [tex]\frac{\sqrt{a^2-a}}{\sqrt{a-1}}[/tex]

    You don't need to multiply by anything, you just need to factor a2-a
     
  6. Oct 7, 2008 #5

    Redbelly98

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    What is the common factor in a2-a?
     
  7. Oct 7, 2008 #6

    thrill3rnit3

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    lol I'm laughing at myself right now...
     
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