Results 1 to 2 of 2

Thread: How To Simplify...?

  1. #1
    Member
    Joined
    Apr 2008
    Posts
    123

    How To Simplify...?

    Why does #1 become #2 and how?

    #1

    ((3-x)^3)/(3x^(2/3)) - 3((3-x)^2)(x^(1/3))

    #2

    -(((x-3)^2)(10x-3))/(3x^(2/3))

    I multiplied - 3((3-x)^2)(x^(1/3)) by the denominator ((3x^(2/3))), but still don't get why... or how.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    12,028
    Thanks
    849
    Hello, AlphaRock!

    Why does #1 become #2 and how?

    #1: .$\displaystyle \frac{(3-x)^3}{3x^{\frac{2}{3}}} - 3(3-x)^2x^{\frac{1}{3}}$

    #2: .$\displaystyle -\,\frac{(x-3)^2(10x-3)}{3x^{\frac{2}{3}}} $
    We have: .$\displaystyle \frac{(3-x)^2}{3x^{\frac{2}{3}}} - 3(3-x)^2x^{\frac{1}{3}} $

    Get a common denominator: .$\displaystyle \frac{(3-x)^3}{3x^{\frac{1}{3}}} \;- \;\frac{3(3-x)^2x^{\frac{1}{3}}}{1}\cdot{\color{blue}\frac{3x^ {\frac{2}{3}}}{3x^{\frac{2}{3}}}} $

    . . . . . $\displaystyle = \;\;\frac{(3-x)^3}{3x^{\frac{2}{3}}} - \frac{9x(3-x)^2}{3x^{\frac{2}{3}}} \;\;=\;\;\frac{(3-x)^3 - 9x(3-x)^2}{3x^{\frac{2}{3}}} $

    Factor: .$\displaystyle \frac{(3-x)^2\bigg[(3-x) - 9x\bigg]}{3x^{\frac{2}{3}}} \;\;=\;\;\frac{(3-x)^2\bigg[-10x + 3\bigg]}{3x^{\frac{2}{3}}}$

    Factor out -1: .$\displaystyle -\,\frac{(x-3)^2(10x-3)}{3x^{\frac{2}{3}}} $

    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. simplify #2
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: Sep 21st 2009, 02:37 PM
  2. Please simplify
    Posted in the Trigonometry Forum
    Replies: 4
    Last Post: Apr 27th 2009, 04:32 AM
  3. Can you simplify this further?
    Posted in the Algebra Forum
    Replies: 4
    Last Post: Apr 23rd 2009, 06:45 AM
  4. Simplify
    Posted in the Algebra Forum
    Replies: 2
    Last Post: Apr 12th 2009, 05:06 AM

Search Tags


/mathhelpforum @mathhelpforum