Partial Fraction Decomposition w/ Substitute Numerators

Pre-Calculus Tutorial

Partial Fraction Decomposition w/ Substitute Numerators

Intro

Partial Fraction Decomposition: the process of starting with the simplified answer and taking it back apart, or “decomposing” the final expression into its initial polynomial fractions. With this tutorial, you’ll learn how to set up an equation that will help you to solve problems like these.

Sample Problem

Here we have the fraction:

f(x)/(x^2+4x+3)=

What two fractions make up this one (use A and B as the numerators)?

(A+B)/[(x+1)+(x+3)]


A/(x+1)+B/x+3


A/(x^2+4x+3)+B/(x^2+4x+3)


Solution

Step 1: Determine the factors of the denominators

x^2+4x+3=(x+1)(x+3)

Step 2: Since we don’t know the value of f(x), we use A & B as our substitute numerators

f(x)/(x^2+4x+3)=A/(x+1)+B/(x+3)

Reminder: This is only a tutorial on how to set up equations for Partial Fraction Decomposition, not on how to solve them.



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