Results 1 to 4 of 4

Math Help - Rationalizing a radical expression

  1. #1
    Newbie
    Joined
    May 2011
    Posts
    24

    Rationalizing a radical expression

    Hello everyone I am needing some help with rationalizing and expression.

    This is what I currently have:
    \frac{-5}{2(x-5)^2\sqrt{\frac{x}{(x-5}}}

    now I multiplied both sides by \sqrt{\frac{x}{(x-5)}}

    got  \frac{-5 \sqrt{\frac{x}{x-5}}}{\frac{2x(x-5)^2}{(x-5)}}

    I canceled out the terms and got \frac{-5 \sqrt \frac{x}{(x-5)}}{2x(x-5)}

    Now I have no idea what to do with the expression in the numerator. Any help would be appreciated and Thanks in advance!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member
    Joined
    Jun 2012
    From
    Georgia
    Posts
    179
    Thanks
    22

    Re: Rationalizing a radical expression

    Obviously the denominator is done. Now think about what methods can be used to rationalize the x-5 term in the numerator, and select one that works.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,683
    Thanks
    614

    Re: Rationalizing a radical expression

    Hello, DjNito!

    \text{Simplify and rationalize: }\:\dfrac{-5}{2(x-5)^2\sqrt{\dfrac{x}{x-5}}}

    I would do it like this . . .

    \dfrac{-5}{2(x-5)^2\cdot\dfrac{x^{\frac{1}{2}}}{(x-5)^{\frac{1}{2}}}}  \;=\;\dfrac{-5}{3(x-5)^{\frac{3}{2}}x^{\frac{1}{2}}}


    Multiply by \frac{x^{\frac{1}{2}}(x-5)^{\frac{1}{2}}}{x^{\frac{1}{2}}(x-5)^{\frac{1}{2}}}:\;\; \dfrac{-5}{3(x-5)^{\frac{3}{2}}x^{\frac{1}{2}}} \cdot \frac{x^{\frac{1}{2}}(x-5)^{\frac{1}{2}}}{x^{\frac{1}{2}}(x-5)^{\frac{1}{2}}}

    . . . . . =\; \dfrac{-5x^{\frac{1}{2}}(x-5)^{\frac{1}{2}}}{3x(x-5)^2} \;=\; \dfrac{-5\sqrt{x(x-5)}}{3x(x-5)^2}
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,404
    Thanks
    1293

    Re: Rationalizing a radical expression

    Quote Originally Posted by DjNito View Post
    Hello everyone I am needing some help with rationalizing and expression.

    This is what I currently have:
    \frac{-5}{2(x-5)^2\sqrt{\frac{x}{(x-5}}}

    now I multiplied both sides by \sqrt{\frac{x}{(x-5)}}

    got  \frac{-5 \sqrt{\frac{x}{x-5}}}{\frac{2x(x-5)^2}{(x-5)}}

    I canceled out the terms and got \frac{-5 \sqrt \frac{x}{(x-5)}}{2x(x-5)}

    Now I have no idea what to do with the expression in the numerator. Any help would be appreciated and Thanks in advance!
    \displaystyle \begin{align*} -\frac{5}{2 \left( x - 5 \right) ^2 \sqrt{ \frac{x}{x - 5} }} &= -\frac{5}{2(x-5)^2}\left( \frac{1}{\sqrt{\frac{x}{x-5}}} \right) \\ &= -\frac{5}{2(x - 5)^2} \left( \frac{1}{\frac{\sqrt{x}}{\sqrt{x-5}}} \right) \\ &= -\frac{5}{2(x-5)^2} \left( \frac{\sqrt{x-5}}{\sqrt{x}} \right) \\ &= -\frac{5\,\sqrt{x}\,\sqrt{x-5}}{2x \left(x-5 \right)^2} \end{align*}
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 2
    Last Post: March 18th 2012, 07:35 PM
  2. Radical Expression
    Posted in the Algebra Forum
    Replies: 2
    Last Post: January 9th 2011, 10:06 AM
  3. radical expression
    Posted in the Algebra Forum
    Replies: 1
    Last Post: May 10th 2010, 07:27 PM
  4. Radical Expression
    Posted in the Algebra Forum
    Replies: 6
    Last Post: April 29th 2010, 06:21 PM
  5. Help with radical expression!!!
    Posted in the Algebra Forum
    Replies: 7
    Last Post: September 10th 2008, 06:31 AM

Search Tags


/mathhelpforum @mathhelpforum