Partial Fraction Expansion: Linear Factors

Partial Fraction Expansion (PFE) renames a fraction of polynomials using smaller, simpler ‘pieces’.
The preceding section introduces PFE, reviews all needed concepts, and presents a simple example (distinct linear factors).
This current section builds on that one, giving:

Summary: The Complete ‘How-To’ of Partial Fraction Expansion

PFE Example: Repeated Linear Factors

Find the partial fraction expansion of $\displaystyle\,\frac{3x^2 + 15x + 8}{(x+1)^2(x-3)}\,$.

Here, the denominator (a cubic polynomial) is already completely factored—rejoice!
The denominator has one distinct linear factor, $\,x-3\,$, and a repeated linear factor, $\,(x+1)^2\,$.

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

When you're done practicing, move on to:
PFE: Irreducible Quadratic Factors

On this exercise, you will not key in your answer.
However, you can check to see if your answer is correct.
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(MAX is 6; there are 6 different problem types.)
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