Meaning of partial quotients

Answer 1

If you have a ratio of polynomials in which the denominator can be factorised, then partial quotients or partial fractions are form an equivalent expression but one in which the denominators of the terms are those fractions.

For example, suppose you start with (2x + 5)/(x^2 + 3x + 2)

The denominator can be factorised into (x + 1)*(x + 2)

So the partial fractions are 3/(x + 1) - 1/((x + 2).