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Math Help - Manipulating Fractions

  1. #1
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    Manipulating Fractions

    I'm trying to do an intergration using the t-substitution so I've been reading examples and I keep loosing track on a similar fraction problem. I don't understand how
    \frac{4}{3+(10t/(1+t^2))} * \frac{2}{1+t^2} = \frac{8}{3t^2+10t+3}

    Any insight on how you can manipulate this is greatly appreciated

    Cheers,
    Isk
    Last edited by Isktaine; November 15th 2008 at 12:51 PM.
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  2. #2
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  3. #3
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    {\color{red}\frac{4}{3 + \displaystyle \frac{10t}{(1+t^2)}}} \ \cdot \ {\color{blue}\frac{2}{1+t^2}}

    To multiply fractions, simply multiply numerator by numerator and denominator by denominator:

     = \frac{{\color{red}4} \cdot {\color{blue}2}}{{\color{red}\left(3 + \displaystyle \frac{10t}{(1+t^2)}\right)}{\color{blue}\left(1+t^  2\right)}}

    You should know that: a(b+c) = ab + ac. Here, imagine a = {\color{blue}1+t^2}.

    So, simplifying:
    = \frac{8}{{\color{red}3}{\color{blue}(1+t^2)} + \displaystyle \frac{{\color{red}10t}}{{\color{blue}1+t^2}} {\color{blue}\left(1+t^2\right)}}

    Notice that in the denominator, the 1 + t^2 cancels out in the second term, so we get:

    = \frac{8}{3(1+t^2) + 10t}

    and so on and so on ..
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  4. #4
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    Thank you soo much!
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