SS3 First Term Further Mathematics Lesson Note – Partial Fractions

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WEEK 3

TOPIC: PARTIAL FRACTIONS

CONTENT:

• Basic definitions
• Proper rational functions with linear factors (distinct and repeated)

Subtopic 1: Basic Definitions

You know what a fraction is. ¼ is a fraction. When we have 3/5 + 2/x, , we say that 3/5 and 2/x are the partial fractions of

Let p(x) and q(x) be polynomials in a variable x.  is called a rational fraction in q(x) ≠ 0.

When the degree of p(x) is less than the degree of q(x), then the rational function is called a proper rational function.

Any rational function can be expressed as the sum of a polynomial function and a proper rational function.

Note that the sum and difference of two rational functions is a rational function.

Example:

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