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Expanding Exponent Expressions

  1. Apr 12, 2008 #1
    Hi, I don know how to go about expanding things such as

    apparently that equals 12x^{2} - 4x

    i know that [tex]3x\sqrt{3x-1}[/tex] can be written as [tex]3x(3x-1)^{\frac{1}{2}}[/tex]

    but i dont know what to do. I cant remeber.

    Thanks :)
  2. jcsd
  3. Apr 12, 2008 #2
    [tex]3x\sqrt{3x-1} \neq 12x^2 - 4x[/tex]
  4. Apr 12, 2008 #3
    SORRY MY BAD I MENT [tex]2x\sqrt{3x-1}[/tex] = 12x^{2} - 4x

    How do i get there?

    Thanks :)
  5. Apr 12, 2008 #4
    [tex]2x\sqrt{3x-1} \neq 12x^2 - 4x[/tex]
  6. Apr 13, 2008 #5
    SORRY. Ill start a bit further back
    i have this:

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

    and I dont know how it simplifies to

    [tex]\frac{3x^{2} + 12x^{2} - 4x}{2\sqrt{3x-1}}[/tex]

    I cant see that the
    [tex]x^{2} x \frac{3}{2}(2x-1)^{-\frac{1}{2}} [/tex] will equal [tex]\frac{3x^{2}}{2\sqrt{3x-1}}[/tex]

    but i cant see how the other bit simplifies... can you show me

    Last edited: Apr 13, 2008
  7. Apr 13, 2008 #6


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    Hi thomas49th! :smile:

    Do you follow:

    [tex]= \frac{3x^{2}}{2\sqrt{3x-1}}\,+\,\frac{2x(3x-1)}{\sqrt{3x-1}}[/tex] ? :smile:
  8. Apr 13, 2008 #7
    yes i can see a common denomitor so u multiply both the numerator and demonitor by [tex]2\sqrt{3x-1}[/tex] of the fraction
    Cheerz :)
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