Results 1 to 2 of 2

Thread: Simplifing

  1. #1
    Junior Member
    Joined
    Jun 2008
    Posts
    39

    Simplifing

    (50x+25/x^2)/((2)sqrt[25x^2-(25/x)]

    simplified = 5(2x^3+1)/((2)sqrt[x^3(x^3-1))]

    I need help on simplifying top to bottom - cannot figure how to get there!!!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Moo
    Moo is offline
    A Cute Angle Moo's Avatar
    Joined
    Mar 2008
    From
    P(I'm here)=1/3, P(I'm there)=t+1/3
    Posts
    5,618
    Thanks
    6
    Hello

    First of all, thank you very much because you put the brackets just like you had to do !
    Quote Originally Posted by weezie23 View Post
    (50x+25/x^2)/((2)sqrt[25x^2-(25/x)]

    simplified = 5(2x^3+1)/((2)sqrt[x^3(x^3-1))]

    I need help on simplifying top to bottom - cannot figure how to get there!!!
    Now, the problem ^^

    $\displaystyle F=\frac{50x+\frac{25}{x^2}}{2 \sqrt{25x^2-\frac{25}{x}}}$

    You can notice that in the solution, there is no more 25 or 50, etc... So we'll simplify by factoring as much as possible

    $\displaystyle F=\frac{25 \left(2x+\frac{1}{x^2}\right)}{2 \cdot \sqrt{25 \left(x^2-\frac 1x\right)}}$

    But $\displaystyle \sqrt{25}=5$ so :

    $\displaystyle F=\frac{5 \cdot 5 \cdot \left(2x+\frac{1}{x^2}\right)}{2 \cdot 5 \cdot \sqrt{x^2-\frac 1x}}$

    Simplify by 5 :

    $\displaystyle F=\frac{5 \cdot \left({\color{red}2x+\frac{1}{x^2}}\right)}{2 \sqrt{x^2-\frac 1x}}$


    Now, you can notice that the red term is very similar to what you want to get : $\displaystyle 2x^3+1$.
    Actually, $\displaystyle 2x^3+1=x^2 \cdot \left({\color{red}2x+\frac{1}{x^2}}\right)$.

    This gives you the trick : multiply the denominator & the numerator by $\displaystyle x^2$


    ---> $\displaystyle F=\frac{5 \cdot (2x^3+1)}{2 \cdot x^2 \cdot \sqrt{x^2-\frac 1x}}$

    But $\displaystyle x^2=\sqrt{x^4}$.


    $\displaystyle \implies F=\frac{5 \cdot (2x^3+1)}{2 \cdot \sqrt{x^4 \left(x^2-\frac 1x\right)}}$


    $\displaystyle F=\frac{5 \cdot (2x^3+1)}{2 \cdot \sqrt{x^3(x^3-1)}}$






    Is it clear enough ?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. simplifing expressions
    Posted in the Math Topics Forum
    Replies: 3
    Last Post: Jan 30th 2010, 12:16 PM
  2. Simplifing
    Posted in the Algebra Forum
    Replies: 2
    Last Post: Jul 28th 2009, 08:53 AM
  3. Simplifing to get the 2 values of x
    Posted in the Algebra Forum
    Replies: 4
    Last Post: Mar 14th 2009, 03:47 AM
  4. I need help simplifing this eqaution.
    Posted in the Algebra Forum
    Replies: 2
    Last Post: Mar 3rd 2008, 02:57 PM
  5. simplifing exponent
    Posted in the Algebra Forum
    Replies: 5
    Last Post: Oct 24th 2007, 10:30 AM

Search Tags


/mathhelpforum @mathhelpforum