Partial Fraction Expansion: Irreducible Quadratic Factors

Partial Fraction Expansion (PFE) renames a fraction of polynomials (i.e., a rational function), using smaller, simpler ‘pieces’.
This is the third of three sections covering PFE:

The steps indicated in the examples below follow the summary of the previous section.

PFE with an initial long division, factoring a difference of cubes,
and distinct irreducible quadratic factor

Find the partial fraction expansion of   $\displaystyle \frac{2x^4 + 4x^2 - 5x + 2}{x^3 - 1} \,$.

Example: PFE with a Repeated Irreducible Quadratic Factor

Find the partial fraction expansion of $\displaystyle\,\frac{3x^2 - 5}{x^4 + 6x^2 + 9}\,$.

(The following solution is much more compact than the prior example.)

Master the ideas from this section
by practicing the exercise at the bottom of this page.

When you're done practicing, move on to:
Introduction to Conic Sections

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