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Math Help - Simplifing

  1. #1
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    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!!!
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  2. #2
    Moo
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    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 ^^

    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

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

    But \sqrt{25}=5 so :

    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 :

    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 : 2x^3+1.
    Actually, 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 x^2


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

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


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


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






    Is it clear enough ?
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