Results 1 to 2 of 2

Math Help - How to simplify algebraic expression

  1. #1
    Member
    Joined
    Jan 2010
    Posts
    106
    Thanks
    2

    How to simplify algebraic expression

    \frac{1}{(\frac{x - 3}{x - 2})^{\frac{1}{2}}} \cdot \frac{1}{2}(\frac{x - 3}{x - 2})^{-\frac{1}{2}} \cdot \frac{1}{(x - 2)^{2}}

    \frac{1}{(\frac{x - 3}{x - 2})^{\frac{1}{2}}} \cdot \frac{1}{2}(\frac{x - 3}{x - 2})^{-\frac{1}{2}} \cdot \frac{1}{(x - 2)^{2}} \\<br />
\frac{1}{(\frac{x - 3}{x - 2})^{\frac{1}{2}}} \cdot \frac{1}{2}\frac{1}{(\frac{x - 3}{x - 2})^{\frac{1}{2}}} \cdot \frac{1}{(x - 2)^{2}} \\<br />
\frac{1}{(\frac{x - 3}{x - 2})^{\frac{1}{2}}} \cdot \frac{\frac{1}{2}}{(\frac{x - 3}{x - 2})^{\frac{1}{2}}} \cdot \frac{1}{(x - 2)^{2}} \\<br />
\frac{1}{(\frac{x - 3}{x - 2})^{\frac{1}{2}}} \cdot \frac{1}{2(\frac{x - 3}{x - 2})^{\frac{1}{2}}} \cdot \frac{1}{(x - 2)^{2}} \\<br />
\frac{1}{(\frac{x - 3}{x - 2})^{\frac{1}{2}}} \cdot \frac{1}{(\frac{x - 3}{x - 2})^{\frac{1}{2}}} \cdot \frac{1}{2(x - 2)^{2}} \\<br />
\frac{1}{(\frac{x - 3}{x - 2})} \cdot \frac{1}{2(x - 2)^{2}} \\<br />
\frac{1}{(x - 3)} \cdot \frac{1}{2(x - 2)} \\<br />
\frac{1}{2(x - 3)(x - 2)}

    Which step have I done incorrectly?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,914
    Thanks
    777

    Re: How to simplify algebraic expression

    Hello, daigo!

    Your answer is correct.
    You made a few unnecessary steps, though.


    \frac{1}{\left(\dfrac{x - 3}{x - 2}\right)^{\frac{1}{2}}} \cdot \frac{1}{2}\left(\frac{x - 3}{x - 2}\right)^{-\frac{1}{2}} \cdot \frac{1}{(x - 2)^{2}}

    \text{We have: }\;\frac{1}{2}\cdot\underbrace{\frac{1}{\left( \dfrac{x-3}{x-2}\right)^{\frac{1}{2}}}\cdot \frac{1}{\left(\dfrac{x-3}{x-2}\right)^{\frac{1}{2}}}}_{\downarrow} \cdot\frac{1}{(x-2)^2}

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

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

Similar Math Help Forum Discussions

  1. Factor and Simplify Algebraic Expression
    Posted in the Algebra Forum
    Replies: 14
    Last Post: June 25th 2012, 06:59 PM
  2. Replies: 7
    Last Post: November 10th 2011, 12:57 PM
  3. Replies: 6
    Last Post: October 6th 2011, 02:48 PM
  4. Factor and Simplify Algebraic Expression
    Posted in the Algebra Forum
    Replies: 2
    Last Post: December 29th 2009, 01:30 PM
  5. Factor and simplify the algebraic expression
    Posted in the Algebra Forum
    Replies: 1
    Last Post: November 14th 2009, 08:47 AM

Search Tags


/mathhelpforum @mathhelpforum