Explanation Given: The rational expression is, 4 m 3 m 2 + 7 m − 6 − m 3 m 2 − 14 m + 8 . Property used: Fundamental property, P Q = P S Q S , for all mathematical expressions P , Q , R , and S , with Q ≠ 0 and S ≠ 0 . Subtraction property, P Q − R Q = P − R Q , for all mathematical expressions P , Q , and R , with Q ≠ 0 . Calculation: Since the denominators of the two rational expressions are different, take least common denominator and then add the numerator while keeping the same denominator. Obtain the factors of the denominators. 3 m 2 + 7 m − 6 = 3 m 2 − 2 m + 9 m − 6 = m ( 3 m − 2 ) + 3 ( 3 m − 2 ) = ( 3 m − 2 ) ( m + 3 ) 3 m 2 − 14 m + 8 = 3 m 2 − 2 m − 12 m + 8 = m ( 3 m − 2 ) − 4 ( 3 m − 2 ) = ( 3 m − 2 ) ( m − 4 ) Thus, the rational expression becomes, 4 m ( 3 m − 2 ) ( m + 3 ) − m ( 3 m − 2 ) ( m − 4 ) . The least common denominator of ( 3 m − 2 ) ( m + 3 ) and ( 3 m − 2 ) ( m − 4 ) is ( m + 3 ) ( 3 m − 2 ) ( m − 4 ) . Multiply the first term by ( x − 2 ) ( x − 2 ) and the second term by ( x + 3 ) ( x + 3 ) and apply Fundamental property as follows. 4 m 3 m 2 + 7 m − 6 − m 3 m 2 − 14 m + 8 = 4 m ( 3 m − 2 ) ( m + 3 ) ⋅ ( m − 4 ) ( m − 4 ) − m ( 3 m − 2 ) ( m − 4 ) ⋅ ( m + 3 ) ( m + 3 ) Simplify the terms as follows, 4 m 3 m 2 + 7 m − 6 −

Finite Mathematics and Calculus with Applications Books a la Carte Plus MyLab Math Package (10th Edition)

10th Edition

ISBN: 9780133935592

Author: Margaret L. Lial, Raymond N. Greenwell, Nathan P. Ritchey

Publisher: PEARSON

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Chapter R.3, Problem 36E

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To express: The rational expression 4m3m2+7m−6−m3m2−14m+8 in lowest terms.

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Chapter R.3, Problem 35E

Chapter R.3, Problem 37E

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Finite Mathematics and Calculus with Applications Books a la Carte Plus MyLab Math Package (10th Edition)

Ch. R.1 - Perform the operation 3(x24x5)4(3x25x7)Ch. R.1 - Perform the operation (3y+2)(4y22y5).Ch. R.1 - Find (2x+7)(3x1) using the FOIL method.Ch. R.1 - Find (3x+2y)3.Ch. R.1 - Perform the indicated operations....Ch. R.1 - Perform the indicated operations....Ch. R.1 - Perform the indicated operations....Ch. R.1 - Perform the indicated operations....Ch. R.1 - Perform the indicated operations....Ch. R.1 - Perform the indicated operations....

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To express: The rational expression 4 m 3 m 2 + 7 m − 6 − m 3 m 2 − 14 m + 8 in lowest terms.

Solution Summary: The author explains the rational expression, m(3m-19), and the subtraction property.

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To express: The rational expression 4m3m2+7m−6−m3m2−14m+8 in lowest terms.

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Chapter R Solutions