m²+3m+2 m²+5m+6 m²+5m+4 m²+10m+24

Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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The given mathematical expression is a rational expression that involves division between two fractions. Here is the transcribed expression:

\[\frac{m^2 + 3m + 2}{m^2 + 5m + 4} \div \frac{m^2 + 5m + 6}{m^2 + 10m + 24}\]

The expression can be broken down as follows:

1. The first fraction is:
   \[\frac{m^2 + 3m + 2}{m^2 + 5m + 4}\]

2. The second fraction is:
   \[\frac{m^2 + 5m + 6}{m^2 + 10m + 24}\]

3. These two fractions are connected by a division operator (÷). 

To solve this, you would typically rewrite the division of fractions as multiplication by the reciprocal, leading to:

\[\frac{m^2 + 3m + 2}{m^2 + 5m + 4} \times \frac{m^2 + 10m + 24}{m^2 + 5m + 6}\]

At this point, you could factorize the polynomials in the numerators and denominators to simplify the expression further.

Educationally, understanding this process involves:

1. Knowing how to handle division of fractions.
2. Understanding polynomial factorization.
3. Simplifying rational expressions.

This sequence helps to showcase various fundamental algebraic skills.
Transcribed Image Text:The given mathematical expression is a rational expression that involves division between two fractions. Here is the transcribed expression: \[\frac{m^2 + 3m + 2}{m^2 + 5m + 4} \div \frac{m^2 + 5m + 6}{m^2 + 10m + 24}\] The expression can be broken down as follows: 1. The first fraction is: \[\frac{m^2 + 3m + 2}{m^2 + 5m + 4}\] 2. The second fraction is: \[\frac{m^2 + 5m + 6}{m^2 + 10m + 24}\] 3. These two fractions are connected by a division operator (÷). To solve this, you would typically rewrite the division of fractions as multiplication by the reciprocal, leading to: \[\frac{m^2 + 3m + 2}{m^2 + 5m + 4} \times \frac{m^2 + 10m + 24}{m^2 + 5m + 6}\] At this point, you could factorize the polynomials in the numerators and denominators to simplify the expression further. Educationally, understanding this process involves: 1. Knowing how to handle division of fractions. 2. Understanding polynomial factorization. 3. Simplifying rational expressions. This sequence helps to showcase various fundamental algebraic skills.
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