Explanation Given information: The provided mathematical expression is; 2 m 2 + 59 m − 30 m 2 − 10 m + 25 ÷ 2 m 2 − 21 m + 10 m 2 + m − 30 Formula used: To divide by a rational expression, multiply by its reciprocal as; A B ÷ C D = A B ⋅ D C = A D B C Calculation: The provided mathematical expression is; 2 m 2 + 59 m − 30 m 2 − 10 m + 25 ÷ 2 m 2 − 21 m + 10 m 2 + m − 30 To find the reciprocal of expression 2 m 2 − 21 m + 10 m 2 + m − 30 interchange the numerator and denominator as; m 2 + m − 30 2 m 2 − 21 m + 10 Now, the division can be performed by use of formula A B ÷ C D = A B ⋅ D C as; 2 m 2 + 59 m − 30 m 2 − 10 m + 25 ÷ 2 m 2 − 21 m + 10 m 2 + m − 30 = 2 m 2 + 59 m − 30 m 2 − 10 m + 25 ⋅ m 2 + m − 30 2 m 2 − 21 m + 10 Now factor the numerator term 2 m 2 + 59 m − 30 as; 2 m 2 + 59 m − 30 = 2 m 2 + 60 m − m − 30 = 2 m ( m + 30 ) − 1 ( m + 30 ) = ( m + 30 ) ( 2 m − 1 ) Now factor another numerator term m 2 + m − 30 as; m 2 + m − 30 = m 2 + 6 m − 5 m − 30 = m ( m + 6 ) − 5 ( m + 6 ) = ( m + 6 ) ( m − 5 ) And denominator term m 2 − 10 m + 25 can be factorized as; m 2 − 10 m + 25 = m 2 − 5 m − 5 m + 25 = m ( m − 5 ) − 5 ( m − 5 ) = ( m − 5 ) ( m − 5 ) And another denominator term 2

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Chapter 6.2, Problem 68ES

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To calculate: The simplified of expression 2m2+59m−30m2−10m+25÷2m2−21m+10m2+m−30 by division.

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Chapter 6.2, Problem 67ES

Chapter 6.2, Problem 69ES

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Ch. 6.1 - Prob. 1YT Ch. 6.1 - Prob. 2YT Ch. 6.1 - Prob. 3YT Ch. 6.1 - Prob. 4YT Ch. 6.1 - Prob. 5YT Ch. 6.1 - Prob. 6YT Ch. 6.1 - Prob. 1CYU Ch. 6.1 - Prob. 2CYU Ch. 6.1 - Prob. 3CYU Ch. 6.1 - Prob. 4CYU

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The simplified of expression 2 m 2 + 59 m − 30 m 2 − 10 m + 25 ÷ 2 m 2 − 21 m + 10 m 2 + m − 30 by division.

Solution Summary: The author explains how the simplified expression of expression 2 is divided by a rational expression by multiplying by its reciprocal.

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To calculate: The simplified of expression 2m2+59m−30m2−10m+25÷2m2−21m+10m2+m−30 by division.

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Chapter 6 Solutions