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1. Warm-Up 4/2 H

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Rigor: You will learn how to write partial fraction decompositions of rational expressions. Relevance: You will be able to use partial fraction decompositions of rational expression to solve real world problems.

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6-4a Partial Fractions

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Partial Fraction Decomposition the sum of these partial fractions. Partial Fraction is each fraction in the sum.

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Steps to Partial Fraction Decomposition When there are Nonrepeated Linear Factors in the denominator When the degree of the numerator is greater than or equal to the degree of the denominator 1.If the degree of the numerator is greater than or equal to the degree of the denominator you must use long division first to rewrite the expression. 2.Factor the denominator and rewrite fraction as partial fractions with constant numerators, A and B, and the linear factors as denominators. 3.Multiply the equation by the Least Common Denominator. 4.Group like terms. 5.Write the linear system of equations and solve the system for A and B. 6.Then substitute in the values for A and B.

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Example 1: Find the partial fraction decomposition. LCD:

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Example 2: Find the partial fraction decomposition. LCD:

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math! 6-4a Assignment: TX p402, 2-12 even

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