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I'm only just now learning about partial fractions to solve integrals. I've read that

$$\frac{f(x)}{(px^2+qx+r)(x-a)}\equiv \frac{Ax+B}{(px^2+qx+r)}+\frac{C}{(x-a)}$$

I haven't figured out how it was decided that $Ax+B$ ought to be used and why it works. Can someone explain it?

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    Where does everything live? Is $f$ a polynomial? Or even constant? Are $A$ and $B$ constants? And what do you mean by $\equiv$ as opposed to $=$?2012-09-05

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