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Partial Fractions7.4

JMerrill, 2010

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Decomposing Rational Expressions

• We will need to work through these by hand in class.

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Guidelines

• 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

1. If the rational expression is proper (n < d), factor the denominator

2. 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

• YouTube has some great tutorials:

• http://www.youtube.com/watch?v=S-XKGBesRzk