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Math Help - Rationalizing Denominator

  1. #1
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    Question Rationalizing Denominator

    Doing some simple antiderivatives and I wanted to rationalize the denominator of one of the questions to eventually expand the expression:

    QUESTION: (2 + x^2)/(1 + x^2), find the antiderivative

    *So i mulitiplied the expression by (1-x^2)/(1-x^2) which is technically = to 1

    *I ended up with 1 - x^4 in the denominator still and it seems i'm unable to cancel this, I was meaning to end up with my expression all over 1

    Am I rationalizing the denominator correctly? Or in this particular question are u unable to rationalize the denominator?

    Thanks!
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  2. #2
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    Re: Rationalizing Denominator

    Quote Originally Posted by FinkieMufu View Post
    Or in this particular question are u unable to rationalize the denominator?
    Right, because it's already rational!

    You're expected to do long division or else the numerator give-and-take manouvre. I.e. re-write the numerator as 1 + x^2 + 1, and you should be able to see a good place to split the fraction into two...
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  3. #3
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    Re: Rationalizing Denominator

    Quote Originally Posted by FinkieMufu View Post
    Doing some simple antiderivatives and I wanted to rationalize the denominator of one of the questions to eventually expand the expression:
    QUESTION: (2 + x^2)/(1 + x^2), find the antiderivative
    It is simply \int {\frac{{2 + x^2 }}{{1 + x^2 }}dx = \int {\left( {1 + \frac{1}{{1 + x^2 }}} \right)dx} } .

    There is nothing to rationalize.
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