P4.2 - Algebra and functions

Decompose rational functions into Partial fractions to include denominators such as partial fractions (denominators not (ax + b)(cx + d)(ex + f) and (ax + b)(cx + d)2. more complicated than repeated linear terms).; The degree of the numerator may equal or exceed the degree of the denominator.; Applications to integration, differentiation and series expansions.; Quadratic factors in the denominator such as (x2 + a), a > 0, are not required.

Use decompose rational functions into partial fractions to connect the rule to the data and decision in the question.

This matters because decompose rational functions into partial fractions determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply decompose rational functions into partial fractions to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: Decompose rational functions into Partial fractions is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.