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Thread: fractions

  1. January 16th 2012, 05:13 PM #1
    Veronica1999
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    fractions

    Could I get some hints for the attached problem?

    Thanks.
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  2. January 17th 2012, 12:26 AM #2
    princeps
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    Re: fractions

    If we make substitution : x=2009 we can write :

    \frac {(x+3)(x+1)(x-1)(x-3)-9}{(x+5)(x+1)(x-1)(x-5)+135}=\frac {x^4-10x^2}{x^4-26x^2+160}=\frac {x^4-10x^2}{x^4-16x^2-10x^2+160}=

    =\frac{x^2(x^2-10)}{x^2(x^2-16)-10(x^2-16)}=\frac{x^2}{x^2-16}=\frac {2009^2}{2009^2-4^2}=\frac{2009^2}{2005 \cdot 2013}
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