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,...
Related questions
Question
Rational expression
![**Performed Operation: Multiplication of Rational Expressions**
This task involves performing the multiplication of two given rational expressions. Recall that a rational expression is formed by dividing one polynomial by another polynomial.
**Expression to Multiply:**
\[
\frac{9n^2 - 16}{12n + 36} \times \frac{8n^2 - 72}{3n^2 + 23n - 36}
\]
**Instructions:**
1. **Factor all polynomials** where possible.
2. **Cancel out common factors** from the numerators and denominators before multiplying.
3. Multiply the remaining terms to get the final expression.
4. Make sure your final expression is simplified.
**Solution Steps:**
- Factor each expression:
- Factor \(9n^2 - 16\) (difference of squares).
- Factor \(12n + 36\).
- Factor \(8n^2 - 72\) (common factor).
- Factor \(3n^2 + 23n - 36\) (quadratic trinomial).
- Simplify and multiply:
- Cancel any common factors in the numerators and denominators.
- Multiply the simplified numerators together, and the simplified denominators together.
Finally, input your answer in the provided box: \(\_\_\_\).
**Note:** This multiplication operation is crucial in simplifying complex fractions and finding equivalent forms, which is an essential skill in algebra and calculus.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6c693121-0c53-4461-96bf-03d77f2fd62b%2Fab670d50-dd56-4eb9-aa8c-88344901180e%2Fod5vn3q_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Performed Operation: Multiplication of Rational Expressions**
This task involves performing the multiplication of two given rational expressions. Recall that a rational expression is formed by dividing one polynomial by another polynomial.
**Expression to Multiply:**
\[
\frac{9n^2 - 16}{12n + 36} \times \frac{8n^2 - 72}{3n^2 + 23n - 36}
\]
**Instructions:**
1. **Factor all polynomials** where possible.
2. **Cancel out common factors** from the numerators and denominators before multiplying.
3. Multiply the remaining terms to get the final expression.
4. Make sure your final expression is simplified.
**Solution Steps:**
- Factor each expression:
- Factor \(9n^2 - 16\) (difference of squares).
- Factor \(12n + 36\).
- Factor \(8n^2 - 72\) (common factor).
- Factor \(3n^2 + 23n - 36\) (quadratic trinomial).
- Simplify and multiply:
- Cancel any common factors in the numerators and denominators.
- Multiply the simplified numerators together, and the simplified denominators together.
Finally, input your answer in the provided box: \(\_\_\_\).
**Note:** This multiplication operation is crucial in simplifying complex fractions and finding equivalent forms, which is an essential skill in algebra and calculus.
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Given query is to simplify the expression.
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