Partial fractions rules for simplifying $\frac{P(x)}{Q(x)}$

(Wednesday, September 1, 2021)

1)

If $\mbox{degree of }P\geq\mbox{degree of }Q$ , then do long division first.
2)

For every distinct root $c$ , add a term of the form

$\frac{A}{x-c}.$
3)

For every repeated root of the form $(x-c)^{n}$ , add terms of the form

$\frac{A_{1}}{x-c}+\cdots+\frac{A_{n}}{x-c}^{n}.$
4)

For every quadratic $q(x)$ that cannot be factored, include a term of the form

$\frac{Ax+B}{q(x)}.$

Partial fractions rules for simplifying P⁢(x)Q⁢(x)