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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Question
Simplify the rational expression
![Certainly! Here’s a transcription suitable for an educational website:
---
**2. Simplify the following expression:**
\[
\frac{1 + 12x^{-1} + 27x^{-2}}{x^{-1} + 9x^{-2}}
\]
---
In this expression, we are asked to simplify a rational function that contains negative exponents.
**Numerator:**
- \(1\)
- \(12x^{-1}\) (equivalent to \(\frac{12}{x}\))
- \(27x^{-2}\) (equivalent to \(\frac{27}{x^2}\))
**Denominator:**
- \(x^{-1}\) (equivalent to \(\frac{1}{x}\))
- \(9x^{-2}\) (equivalent to \(\frac{9}{x^2}\))
To simplify, consider factoring and combining like terms where possible, converting negative exponents to fractions for easier manipulation.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F331788ad-f8d4-43b8-aeab-588d8fea9e20%2F35ccfcad-ded5-4cf2-8e7c-c556dc5152b4%2F7e986ju_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Certainly! Here’s a transcription suitable for an educational website:
---
**2. Simplify the following expression:**
\[
\frac{1 + 12x^{-1} + 27x^{-2}}{x^{-1} + 9x^{-2}}
\]
---
In this expression, we are asked to simplify a rational function that contains negative exponents.
**Numerator:**
- \(1\)
- \(12x^{-1}\) (equivalent to \(\frac{12}{x}\))
- \(27x^{-2}\) (equivalent to \(\frac{27}{x^2}\))
**Denominator:**
- \(x^{-1}\) (equivalent to \(\frac{1}{x}\))
- \(9x^{-2}\) (equivalent to \(\frac{9}{x^2}\))
To simplify, consider factoring and combining like terms where possible, converting negative exponents to fractions for easier manipulation.
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