Partial Fractions
If the degree of the numerator is greater than or equal to the degree of the
denominator then use algebraic long division to obtain a rational function.
Distinct Linear Factors
e.g.
2𝑥 + 18
(𝑥 − 5)(𝑥 + 2)
=
𝐴
𝑥−5
+
𝐵
𝑥+2
Irreducible Quadratic Factor
e.g.
2𝑥 + 3
(𝑥 − 1)(𝑥 2 +
=
4)
𝐴
+
𝑥−1
𝐵𝑥 + 𝐶
𝑥2 + 4
Repeated Linear Factor
e.g.
3𝑥 2 − 1
( 𝑥 − 1)(2𝑥 − 1)2
=
𝐴
+
(𝑥 − 1)
𝐵
+
(2𝑥 − 1)
𝐶
(2𝑥 − 1)2