Partial fractions
Decompose 1/[(x-a)(x-b)] into A/(x-a) + B/(x-b). Y13 Pure.
Cover-up method or comparing coefficients. Used to simplify integration and binomial expansion of rational expressions.
Worked examples
1/[(x-1)(x-2)] = -1/(x-1) + 1/(x-2).
(3x+5) / [(x+1)(x-2)] = A/(x+1) + B/(x-2) with A = -2/3, B = 11/3.
Repeated factor: A/(x-1) + B/(x-1)².
Frequently asked questions
Cover-up method?
Set the value that makes a factor zero. The remaining expression evaluated there gives the corresponding numerator.
Why is this useful?
Integration: 1/(x-1) integrates to ln|x-1|. Binomial: each term expands more easily.