Does this make sense?

**DannyMath** · April 4th 2011, 02:11 PM

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)

**TheEmptySet** · April 4th 2011, 02:19 PM

Originally Posted by DannyMath

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

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

**pickslides** · April 4th 2011, 02:20 PM

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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