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
![### Subtraction of Rational Expressions
**Problem:**
Subtract the following rational expressions:
\[
\frac{3x^2 + x - 5}{x^2 - 6x + 9} - \frac{2x - 5}{x^2 - 6x + 9}
\]
**Options:**
A) \(\frac{3x^2 - x - 4}{x^2 - 6x + 9}\)
B) \(\frac{x^2 + 3x + 1}{x^2 - 6x + 9}\)
C) \(\frac{x + 6}{x^2 - 6x + 9}\)
D) \(\frac{3x^2 - x}{x^2 - 6x + 9}\)
**Explanation:**
To subtract these expressions, ensure the denominators are the same, which they are in this case: \(x^2 - 6x + 9\).
1. Combine the numerators:
\[\left(3x^2 + x - 5\right) - \left(2x - 5\right)\]
2. Simplify the expression:
\[3x^2 + x - 5 - 2x + 5\]
3. Combine like terms:
\[3x^2 - x\]
Thus, the simplified expression is:
\[
\frac{3x^2 - x}{x^2 - 6x + 9}
\]
The correct option is D) \(\frac{3x^2 - x}{x^2 - 6x + 9}\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5feef8a3-4722-4969-8d03-b0e4b16fec00%2Fb9405ff9-b2dc-41cf-9c4a-9c7bfebe7ad9%2Fmw3vruf_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Subtraction of Rational Expressions
**Problem:**
Subtract the following rational expressions:
\[
\frac{3x^2 + x - 5}{x^2 - 6x + 9} - \frac{2x - 5}{x^2 - 6x + 9}
\]
**Options:**
A) \(\frac{3x^2 - x - 4}{x^2 - 6x + 9}\)
B) \(\frac{x^2 + 3x + 1}{x^2 - 6x + 9}\)
C) \(\frac{x + 6}{x^2 - 6x + 9}\)
D) \(\frac{3x^2 - x}{x^2 - 6x + 9}\)
**Explanation:**
To subtract these expressions, ensure the denominators are the same, which they are in this case: \(x^2 - 6x + 9\).
1. Combine the numerators:
\[\left(3x^2 + x - 5\right) - \left(2x - 5\right)\]
2. Simplify the expression:
\[3x^2 + x - 5 - 2x + 5\]
3. Combine like terms:
\[3x^2 - x\]
Thus, the simplified expression is:
\[
\frac{3x^2 - x}{x^2 - 6x + 9}
\]
The correct option is D) \(\frac{3x^2 - x}{x^2 - 6x + 9}\).
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