Elementary Algebra
17th Edition
ISBN:9780998625713
Author:Lynn Marecek, MaryAnne Anthony-Smith
Publisher:Lynn Marecek, MaryAnne Anthony-Smith
Chapter8: Rational Expressions And Equations
Section8.3: Add And Subtract Rational Expressions With A Common Denominator
Problem 166E: If Pete can paint a wall in p hours, then in one hour he can paint 1p of the wall. It would take...
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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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5c1b1525-9f55-427c-9418-433680b9f4b9%2Fb1691d73-29dd-4f65-90ec-f6cc7c258251%2Fpt3itaa_processed.png&w=3840&q=75)
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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