Explanation Result used: If the denominators of a rational expression differ, we must find equivalent rational expressions that have a common denominator. To find the least common denominator of rational expressions, factor each denominator and form the product that uses each factor the greatest number of times it occurs in any factorization. Calculation: The given rational expression is, 9 x + 2 3 x 2 − 2 x − 8 + 7 3 x 2 + x − 4 . Factorize the denominator of the rational expression 9 x + 2 3 x 2 − 2 x − 8 + 7 3 x 2 + x − 4 as follows. 9 x + 2 3 x 2 − 2 x − 8 + 7 3 x 2 + x − 4 = 9 x + 2 ( 3 x + 4 ) ( x − 2 ) + 7 ( 3 x + 4 ) ( x − 1 ) By the above result, the least common denominator of the rational expression 9 x + 2 3 x 2 − 2 x − 8 + 7 3 x 2 + x − 4 is ( 3 x + 4 ) ( x − 2 ) ( x − 1 ) . Simplify the expression 9 x + 2 ( 3 x + 4 ) ( x − 2 ) + 7 ( 3 x + 4 ) ( x − 1 ) as follows. 9 x + 2 ( 3 x + 4 ) ( x − 2 ) + 7 ( 3 x + 4 ) ( x − 1 ) = 9 x + 2 ( 3 x + 4 ) ( x − 2 ) ⋅ x − 1 x − 1 + 7 ( 3 x + 4 ) ( x − 1 ) ⋅ x − 2 x − 2 = ( 9 x + 2 ) ( x − 1 ) ( 3 x + 4 ) ( x − 2 ) ( x − 1 )

College Algebra: Graphs and Models (6th Edition)

6th Edition

ISBN: 9780134179032

Author: Marvin L. Bittinger, Judith A. Beecher, David J. Ellenbogen, Judith A. Penna

Publisher: PEARSON

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Chapter J.23, Problem 4E

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To compute: The value of the expression 9x+23x2−2x−8+73x2+x−4.

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Chapter J.23, Problem 3E

Chapter J.23, Problem 5E

Chapter J Solutions

College Algebra: Graphs and Models (6th Edition)

Ch. J.1 - In Exercises 1-6, consider the numbers 23, 6, 3,...Ch. J.1 - In Exercises 16, consider the numbers 23, 6, 3,...Ch. J.1 - In Exercises 16, consider the numbers 23, 6, 3,...Ch. J.1 - In exercises 16, consider the numbers 23, 6, 3,...Ch. J.1 - In Exercises 16, consider the numbers 23, 6, 3,...Ch. J.1 - In Exercises 16, consider the numbers 23, 6, 3,...Ch. J.2 - Name the property illustrated by the sentence. 1....Ch. J.2 - Name the property illustrated by the sentence. 2....Ch. J.2 - Name the property illustrated by the sentence. 3....Ch. J.2 - Prob. 4E

Ch. J.2 - Prob. 5E Ch. J.2 - Prob. 6E Ch. J.2 - Prob. 7E Ch. J.2 - Prob. 8E Ch. J.2 - Prob. 9E Ch. J.2 - Prob. 10E Ch. J.3 - Classify the inequality as true or false. 1. 9 9 Ch. J.3 - Prob. 2E Ch. J.3 - Classify the inequality as true or false. 3. 265 Ch. J.3 - Prob. 4E Ch. J.3 - Prob. 5E Ch. J.3 - Prob. 6E Ch. J.4 - Simplify. 1. |98|Ch. J.4 - Prob. 2E Ch. J.4 - Prob. 3E Ch. J.4 - Prob. 4E Ch. J.4 - Prob. 5E Ch. J.4 - Prob. 6E Ch. J.4 - Prob. 7E Ch. J.4 - Prob. 8E Ch. J.5 - Compute and simplify. 1. 8 (11)Ch. J.5 - Compute and simplify. 2. 310(13)Ch. J.5 - Prob. 3E Ch. J.5 - Prob. 4E Ch. J.5 - Prob. 5E Ch. J.5 - Prob. 6E Ch. J.5 - Prob. 7E Ch. J.5 - Prob. 8E Ch. J.5 - Prob. 9E Ch. J.5 - Prob. 10E Ch. J.5 - Prob. 11E Ch. J.5 - Compute and simplify. 12. 1223 Ch. J.5 - Prob. 13E Ch. J.5 - Prob. 14E Ch. J.5 - Prob. 15E Ch. J.6 - Write interval notation. 1. {x| 5 x 5}Ch. J.6 - Prob. 2E Ch. J.6 - Write interval notation. 3. {x | x 2}Ch. J.6 - Write interval notation. 4. {x | x 3.8}Ch. J.6 - Prob. 5E Ch. J.6 - Prob. 6E Ch. J.6 - Prob. 7E Ch. J.6 - Prob. 8E Ch. J.6 - Prob. 9E Ch. J.6 - Write interval notation for the graph. 10.Ch. J.7 - Simplify. 1. 36 Ch. J.7 - Prob. 2E Ch. J.7 - Prob. 3E Ch. J.7 - Prob. 4E Ch. J.7 - Prob. 5E Ch. J.7 - Prob. 6E Ch. J.7 - Prob. 7E Ch. J.7 - Prob. 8E Ch. J.7 - Prob. 9E Ch. J.7 - Prob. 10E Ch. J.8 - Convert to scientific notation. 1. 18,500,000 Ch. J.8 - Prob. 2E Ch. J.8 - Prob. 3E Ch. J.8 - Prob. 4E Ch. J.8 - Convert to decimal notation. 5.4.3 108 Ch. J.8 - Prob. 6E Ch. J.8 - Convert to decimal notation. 7.6.203 1011 Ch. J.8 - Prob. 8E Ch. J.9 - Calculate. 1. 3 + 18 6 3 Ch. J.9 - Calculate. 2. 5 3 + 8 32 + 4(6 2)Ch. J.9 - Calculate. 3. 5(3 8 32 + 4 6 2)Ch. J.9 - Calculate. 4. 16 4 4 2 256 Ch. J.9 - Calculate. 5. 26 23 210 28 Ch. J.9 - Calculate. 6. 4(86)243+2831+190 Ch. J.9 - Calculate. 7. 64 [(4) (2)]Ch. J.9 - Prob. 8E Ch. J.10 - Determine the degree of the polynomial. 1. 5 x6 Ch. J.10 - Prob. 2E Ch. J.10 - Prob. 3E Ch. J.10 - Prob. 4E Ch. J.10 - Prob. 5E Ch. J.10 - Prob. 6E Ch. J.10 - Prob. 7E Ch. J.10 - Prob. 8E Ch. J.11 - Add or subtract. 1. (8y 1) (3 y)Ch. J.11 - Add or subtract. 2. (3x2 2x x3 + 2) (5x2 8x ...Ch. J.11 - Prob. 3E Ch. J.11 - Prob. 4E Ch. J.11 - Prob. 5E Ch. J.12 - Prob. 1E Ch. J.12 - Prob. 2E Ch. J.12 - Prob. 3E Ch. J.12 - Prob. 4E Ch. J.12 - Prob. 5E Ch. J.12 - Prob. 6E Ch. J.13 - Multiply. 1. (x + 3)2 Ch. J.13 - Multiply. 2. (5x 3)2 Ch. J.13 - Multiply. 3. (2x + 3y)2 Ch. J.13 - Prob. 4E Ch. J.13 - Multiply. 5. (n + 6) (n 6)Ch. J.13 - Prob. 6E Ch. J.14 - Factor out the largest common factor. 1. 3x + 18 Ch. J.14 - Prob. 2E Ch. J.14 - Prob. 3E Ch. J.14 - Prob. 4E Ch. J.14 - Prob. 5E Ch. J.14 - Prob. 6E Ch. J.14 - Prob. 7E Ch. J.14 - Prob. 8E Ch. J.14 - Prob. 9E Ch. J.14 - Prob. 10E Ch. J.14 - Prob. 11E Ch. J.14 - Prob. 12E Ch. J.15 - Factor. 1. 8x2 6x 9 Ch. J.15 - Factor. 2. 10t2 + 4t 6 Ch. J.15 - Factor. 3. 18a2 51a + 15 Ch. J.16 - Factor the difference of squares. 1. z2 81 Ch. J.16 - Factor the difference of squares. 2. 16x2 9 Ch. J.16 - Factor the difference of squares. 3. 7pq4 7py4 Ch. J.16 - Factor the square of a binomial. 4. x2 + 12x + 36 Ch. J.16 - Prob. 5E Ch. J.16 - Factor the square of a binomial. 6. a3 + 24a2 +...Ch. J.16 - Factor the sum or the difference of cubes. 7. x3 +...Ch. J.16 - Factor the sum or the difference of cubes. 8. m3 ...Ch. J.16 - Prob. 9E Ch. J.16 - Prob. 10E Ch. J.17 - Prob. 1E Ch. J.17 - Prob. 2E Ch. J.17 - Prob. 3E Ch. J.17 - Prob. 4E Ch. J.17 - Solve. 5. 7y 1 = 23 5y Ch. J.17 - Prob. 6E Ch. J.17 - Prob. 7E Ch. J.17 - Solve. 8. 5y 4 (2y 10) = 25 Ch. J.18 - Prob. 1E Ch. J.18 - Prob. 2E Ch. J.18 - Prob. 3E Ch. J.18 - Prob. 4E Ch. J.18 - Prob. 5E Ch. J.18 - Prob. 6E Ch. J.19 - Prob. 1E Ch. J.19 - Prob. 2E Ch. J.19 - Prob. 3E Ch. J.19 - Prob. 4E Ch. J.19 - Prob. 5E Ch. J.19 - Prob. 6E Ch. J.19 - Prob. 7E Ch. J.19 - Prob. 8E Ch. J.20 - Prob. 1E Ch. J.20 - Prob. 2E Ch. J.20 - Prob. 3E Ch. J.20 - Prob. 4E Ch. J.20 - Prob. 5E Ch. J.20 - Prob. 6E Ch. J.21 - Prob. 1E Ch. J.21 - Prob. 2E Ch. J.21 - Prob. 3E Ch. J.21 - Prob. 4E Ch. J.21 - Prob. 5E Ch. J.21 - Prob. 6E Ch. J.22 - Prob. 1E Ch. J.22 - Prob. 2E Ch. J.22 - Prob. 3E Ch. J.22 - Prob. 4E Ch. J.22 - Prob. 5E Ch. J.22 - Prob. 6E Ch. J.23 - Prob. 1E Ch. J.23 - Prob. 2E Ch. J.23 - Prob. 3E Ch. J.23 - Prob. 4E Ch. J.23 - Prob. 5E Ch. J.23 - Prob. 6E Ch. J.24 - Simplify. 1. xyyx1y+1x Ch. J.24 - Prob. 2E Ch. J.24 - Prob. 3E Ch. J.24 - Prob. 4E Ch. J.24 - Simplify. 5. abba1a1b Note: b a = 1(a b)Ch. J.25 - Prob. 1E Ch. J.25 - Prob. 2E Ch. J.25 - Prob. 3E Ch. J.25 - Prob. 4E Ch. J.25 - Prob. 5E Ch. J.25 - Prob. 6E Ch. J.25 - Prob. 7E Ch. J.25 - Prob. 8E Ch. J.25 - Prob. 9E Ch. J.25 - Prob. 10E Ch. J.25 - Prob. 11E Ch. J.25 - Prob. 12E Ch. J.25 - Prob. 13E Ch. J.25 - Prob. 14E Ch. J.25 - Prob. 15E Ch. J.25 - Prob. 16E Ch. J.25 - Prob. 17E Ch. J.25 - Prob. 18E Ch. J.25 - Prob. 19E Ch. J.25 - Prob. 20E Ch. J.26 - Prob. 1E Ch. J.26 - Prob. 2E Ch. J.26 - Prob. 3E Ch. J.26 - Prob. 4E Ch. J.26 - Prob. 5E Ch. J.26 - Prob. 6E Ch. J.26 - Prob. 7E Ch. J.26 - Prob. 8E Ch. J.27 - Prob. 1E Ch. J.27 - Prob. 2E Ch. J.27 - Prob. 3E Ch. J.27 - Prob. 4E Ch. J.27 - Prob. 5E Ch. J.27 - Prob. 6E Ch. J.27 - Prob. 7E Ch. J.27 - Convert to exponential notation. 8. x5 Ch. J.27 - Prob. 9E Ch. J.27 - Prob. 10E Ch. J.27 - Prob. 11E Ch. J.28 - Find the length of the third side of each right...Ch. J.28 - Find the length of the third side of each right...Ch. J.28 - Find the length of the third side of each right...Ch. J.28 - Find the length of the third side of each right...Ch. J.28 - Find the length of the third side of each right...

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The value of the expression 9 x + 2 3 x 2 − 2 x − 8 + 7 3 x 2 + x − 4 .

Solution Summary: The author explains how to find the least common denominator of rational expressions.

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To compute: The value of the expression 9x+23x2−2x−8+73x2+x−4.

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Chapter J Solutions