Performing Partial Fraction Decomposition

Tutoring on Performing Partial Fraction Decomposition

Learning Objectives:

Understand to Perform Partial Fraction Decomposition.

Math Tutoring on Performing Partial Fraction Decomposition

The process of considering a rational expression and decomposing or breaking it into simpler rational expressions that we can add or subtract to get the original rational expression is called partial fraction decomposition. If the degree of the numerator is greater than or equal to the degree of the denominator, we perform long division.

 Step 1: Factor the denominator into prime linear or quadratic factors

Step 2: Linear Factors: Each distinct linear factor of the form (px + q) include the term   A/ (ax + b).   For each repeated factor (ax + b)ᵑ we must include n terms of the form : A/ (ax + b)  +  B/(ax + b)²  + C/(ax + b )³  + ………………

In general we have added and simplified rational expressions. Partial-fraction decomposition is the process of starting with the simplified answer and taking it back apart, of "decomposing" the final expression into its initial polynomial fractions.



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Hook Questions:

1.    How do you decompose a fraction?

2.    What is the partial derivative?

3.    How do you complete the square?




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