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Math Help - Does this make sense?

  1. #1
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    Does this make sense?

    I'm working on past finals and for one of the integrals I don't understand how they got to the second step in the solution listed:

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    I don't understand how they went from x^2/(1+x^2) to 1 and 4/(1+x^2) to 3/(1+x^2)
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  2. #2
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    Quote Originally Posted by DannyMath View Post
    I'm working on past finals and for one of the integrals I don't understand how they got to the second step in the solution listed:

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    I don't understand how they went from x^2/(1+x^2) to 1 and 4/(1+x^2) to 3/(1+x^2)
    The either did polynomial long division or rewrote the problem as follows

    \displaystyle \frac{x^2-2x+4}{x^2+1}=\frac{(x^2+1)-2x+3}{x^2+1}=\frac{x^2+1}{x^2+1}+\frac{-2x}{x^2+1}+\frac{3}{x^2+1}
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  3. #3
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    It looks like polynomial long division has been applied here.

    \displaystyle (x^2-2x+4)\div (1+x^2)= 1- \frac{2x+3}{1+x^2}
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