Partial Fractions

Partial Fractions - Name Partial Fractions PARTIAL FRACTION DECOMPOSITION Given a rational expression we will find simpler rational expressions

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Partial Fractions P ARTIAL F RACTION D ECOMPOSITION Given a rational expression, we will find simpler rational expressions whose sum is the given expression. Examples. 5 6 = 1 2 + 1 3 5 x - 6 x ( x + 3) = -2 x + 7 x + 3 Partial Fraction Decomposition Theorem If f ( x ) = p ( x ) q ( x ) is a rational expression in which the degree of the numerator is less than the degree of the denominator, and p ( x ) and q ( x ) have no common factors, then f ( x ) can be decomposed in the form f ( x ) = f 1 ( x ) + f 2 ( x ) + . . . + f n ( x ) where each f i ( x ) has one of the following forms: A ( ax + b ) m or Bx + C ( ax 2 + bx + c ) m NOTE: The procedure for partial fraction decomposition depends on the factorization of the denominator. F OUR P OSSIBLE C ASES: Case 1 Nonrepeated Linear Factors The partial fraction decomposition will contain an expression of the form A x + a for each nonrepeated linear factor of the denominator. Example.

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This note was uploaded on 04/13/2008 for the course MATH 2412 taught by Professor Matroy during the Spring '08 term at Alamo Colleges.

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Partial Fractions - Name Partial Fractions PARTIAL FRACTION DECOMPOSITION Given a rational expression we will find simpler rational expressions

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