Partial fraction decomposition
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Partial fraction decompostion is a theorem in algebra which states that a rational function can be decomposed into a polynomial plus a sum of proper fractions, each of which is either a constant over a power of a linear polynomial or a linear polynomial over a power of an irreducible quadratic polynomial.
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[edit] Statement of theorem
Let f and g be nonzero polynomials. Write g as a product of powers of distinct irreducible polynomials:
There are (unique) polynomials b and aij with 
such that
If 
, then b = 0.
Alternative Statement:
Hopefully this will provide a simpler, and more accessible version of the proof.
[edit] Outline of proof
[edit] Lemma 1
Let f,g and h be nonzero polynomials with f and g coprime. There are polynomials a and b such that 
[edit] Lemma 2
Let f and g be nonzero polynomials and let n be a positive integer. There exist polynomials b and ai with 
such that 
[edit] Generalization to Euclidean domains
More generally, this is true in any Euclidean domain.
