MAT136H1 Lecture Notes - Partial Fraction Decomposition
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7.4 Integration Techniques
Partial Fractions for Rational Functions
Question #1 (Easy): Decompose Rational Function into Partial Fractions
Rational function with factorable denominator can be decomposed into partial fractions. Combining
partial fractions reverses the process and result in the original rational function. Step 1: factor the
denominator. Step 2: write partial fractions with unknown coefficients at numerator. Step 3: solve for
Write the function into partial fraction decomposition.
The denominator can be factored: . This means
the given function can be decomposed into 3 partial fractions:
. Combine the
numerators: . Simplify the left side:
Combine the like powers: .
Then and and
Solve simultaneously, , and
It is like solving a system of linear equations.
Use substitution , then , then
, so . Then since ,
By decomposition, the rational function is equal to the partial fraction:
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