Explanation Calculation: Consider the expression, 3 x 2 − 3 x Note that the degree of an expression is the highest power of the variable in the expression. Here, numerator has degree 0 and denominator has degree 2. Since the degree of the expression written in the numerator is less than the degree of the expression written in the denominator so, the given rational expression is a proper fraction. Factorize the denominator x 2 − 3 x by taking out common factor x common. x 2 − 3 x = x x − 3 Consider that the degree of the factors x and x − 3 is 1 , which is linear. Since the two factors x and x − 3 are linear, write one partial fraction with numerator as an unknown constant for each of the linear factors. Thus, 3 x 2 − 3 x = A x + B x − 3 The least common denominator (LCD) of the terms on the right side is x x − 3 = x 2 − 3 x . So, make the denominators same. A x + B x − 3 = A x − 3 x x − 3 + B x x x − 3 = A x − 3 + B x x 2 − 3 x Thus, 3 x 2 − 3 x = A x − 3 + B x x 2 − 3 x . Now, the denominators on the either side are same. So, equate the numerators to get the basic equation. 3 = A x − 3 + B x To solve the basic equation for the unknowns A and B , substitute real numbers to make the distinct linear factors equal to zero. To calculate the value of A , substitute x = 0 in the basic equation. For x = 0 , 3 = A 0 − 3 + B 0 = − 3 A + 0 − 1 = A Thus, A = − 1

College Algebra Real Mathematics Real People Edition 7

18th Edition

ISBN: 9781305752368

Author: Ron Larson

Publisher: CENGAGE C

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Chapter 6.4, Problem 18E

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Chapter 6.4, Problem 17E

Chapter 6.4, Problem 19E

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College Algebra Real Mathematics Real People Edition 7

Ch. 6.1 - Solve the system of equations. xy=05x3y=6 Ch. 6.1 - A total of $25,000 is invested in two funds paying...Ch. 6.1 - Solve the system of equations. 2x+y=5x2y+3x=1 Ch. 6.1 - Solve the system of equations. 2x+y=32x2+4xy2=0 Ch. 6.1 - Prob. 5ECP Ch. 6.1 - Prob. 6ECP Ch. 6.1 - Prob. 7ECP Ch. 6.1 - Prob. 1E Ch. 6.1 - Prob. 2E Ch. 6.1 - Fill in the blanks. Graphically, solutions of a...

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The form of partial fraction decomposition of the rational expression 3 x 2 − 3 x and check the answer algebraically.

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