Partial Fractions
7.4
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JMerrill, 2010
Decomposing Rational
Expressions
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• We will need to work through these by hand
in class.
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Guidelines
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• The numerator MUST be less than the
denominator in degree if the denominator
can be reduced to linear or repeated linear
factors. If the numerator is the same degree
or greater (than the denominator), you must
do long division.
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Procedures
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2.
If the rational expression is proper (n < d), factor the denominator
Decompose into fractions with a constant numerator
1. If there are repeated factors, you must include each power of
each factor—one factor will have a constant numerator and one
(or more) will have a linear numerator
2. If the denominator is an irreducible quadratic: expand , collect
like terms = polynomial form.
3. 2 polynomials are = if the coefficients of like terms are =. Set
them = and solve.
3. Find LCD (once we use the LCD’s to get the numerators, we drop
the denominators) = basic equation.
4. Choose an x that will make one factors = 0 and solve. Repeat with
the other factor.
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Helpful Videos
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• YouTube has some great tutorials:
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• http://www.youtube.com/watch?v=SXKGBesRzk
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