Explanation Given: The rational expression 3 x 2 − 3 x − 2 ( x + 2 ) ( x − 2 ) 2 = A x + 2 + B x − 2 + C ( x − 2 ) 2 . Calculation: Considering the rational expression 3 x 2 − 3 x − 2 ( x + 2 ) ( x − 2 ) 2 = A x + 2 + B x − 2 + C ( x − 2 ) 2 Multiplying right side of the equation so that all the denominators are same. = A ( x − 2 ) 2 ( x − 2 ) 2 ( x + 2 ) + B ( x + 2 ) ( x − 2 ) ( x + 2 ) ( x − 2 ) 2 + C ( x + 2 ) ( x − 2 ) 2 ( x + 2 ) Now equating both sides of the expression 3 x 2 − 3 x − 2 = A ( x − 2 ) 2 + B ( x + 2 ) ( x − 2 ) + C ( x + 2 ) Let x = − 2 , 0 , 2 , we get the system of equation as, When, x = − 2 , 3 ( − 2 ) 2 − 3 ( − 2 ) − 2 = A ( − 2 − 2 ) 2 + B ( − 2 + 2 ) ( − 2 − 2 ) + C ( − 2 + 2 ) 12 + 6 − 2 = 16 A 16 = 16 A When, x = 0 3 ( 0 ) 2 − 3 ( 0 ) − 2 = A ( 0 − 2 ) 2 + B ( 0 + 2 ) ( 0 − 2 ) + C ( 0 + 2 ) − 2 = 4 A − 4 B + 2 C When, x = 4 3 ( 2 ) 2 −

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ISBN: 9780357156100

Author: Ron Larson

Publisher: Cengage Limited

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Chapter 1.3, Problem 33E

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The partial fraction decomposition of the rational expression 3x2−3x−2(x+2)(x−2)2=Ax+2+Bx−2+C(x−2)2. Solve the system using matrices.

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Chapter 1.3, Problem 32E

Chapter 1.3, Problem 34E

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The partial fraction decomposition of the rational expression 3 x 2 − 3 x − 2 ( x + 2 ) ( x − 2 ) 2 = A x + 2 + B x − 2 + C ( x − 2 ) 2 . Solve the system using matrices.

Solution Summary: The author calculates the partial tion decomposition of the rational expression 3x2-3x-2(x+2

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To calculate:

The partial fraction decomposition of the rational expression 3x2−3x−2(x+2)(x−2)2=Ax+2+Bx−2+C(x−2)2. Solve the system using matrices.

Want to see the full answer?

Chapter 1 Solutions

The partial fraction decomposition of the rational expression 3 x 2 − 3 x − 2 ( x + 2 ) ( x − 2 ) 2 = A x + 2 + B x − 2 + C ( x − 2 ) 2 . Solve the system using matrices.

Solution Summary: The author calculates the partial tion decomposition of the rational expression 3x2-3x-2(x+2

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To calculate: The partial fraction decomposition of the rational expression 3x2−3x−2(x+2)(x−2)2=Ax+2+Bx−2+C(x−2)2. Solve the system using matrices.

Want to see the full answer?

Chapter 1 Solutions

To calculate:

The partial fraction decomposition of the rational expression 3x2−3x−2(x+2)(x−2)2=Ax+2+Bx−2+C(x−2)2. Solve the system using matrices.