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Math Help - I can't figure this operation.

  1. #1
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    I can't figure this operation.

    I can't figure this operation. here is the question with the answer, I just can't figure, how to get there.

    I'm not sure how that 2 got on the denominator, if somebody can tell me the steps they used, I would appreciate that. Thx for the help.
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  2. #2
    Super Member Quacky's Avatar
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    \displaystyle\frac{1}{1+\displaystyle\frac{x^2}{4}  }\times\frac{1}{2}


    =\displaystyle\frac{1}{2+\frac{x^2}{2}}


    =\displaystyle\frac{1}{2+\frac{x^2}{2}}\times 1


    =\displaystyle\frac{1}{2+\frac{x^2}{2}}\times\frac  {2}{2}


    =\displaystyle\frac{2}{4+x^2}
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  3. #3
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    Quote Originally Posted by melvis View Post
    I can't figure this operation. here is the question with the answer, I just can't figure, how to get there.

    I'm not sure how that 2 got on the denominator, if somebody can tell me the steps they used, I would appreciate that. Thx for the help.
    I assume the original function is \displaystyle y = \arctan\left(\frac{x}{2}\right)

    \displaystyle u = \frac{x}{2}

    \displaystyle \frac{d}{dx} \arctan(u) = \frac{1}{1+u^2} \cdot \frac{du}{dx}

    the \displaystyle\frac{1}{2} is \displaystyle \frac{du}{dx}


    \displaystyle \frac{\frac{1}{2}}{1 + \frac{x^2}{4}} \cdot \frac{4}{4} = \frac{2}{4 + x^2}
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  4. #4
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    thx mate
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  5. #5
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    Quote Originally Posted by melvis View Post
    I can't figure this operation. here is the question with the answer, I just can't figure, how to get there.

    I'm not sure how that 2 got on the denominator, if somebody can tell me the steps they used, I would appreciate that. Thx for the help.
    http://screencast.com/t/n2gG1KqR
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  6. #6
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    Quote Originally Posted by melvis View Post
    I can't figure this operation. here is the question with the answer, I just can't figure, how to get there.

    I'm not sure how that 2 got on the denominator, if somebody can tell me the steps they used, I would appreciate that. Thx for the help.
    In order to get rid of the "4" in \frac{x^2}{4} multiply both numerator and denominator by "4".
    \frac{4}{4\left(1+ \frac{x^2}{4}\right)}\frac{1}{2}= \frac{4\left(\frac{1}{2}\right)}{4+ x^2}= \frac{2}{4+ x^2}
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