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
![### Multiply. Show all work to receive credit for your answer.
\[ \frac{x^2 + 2x + 1}{x - 5} \times \frac{x^2 - 25}{x^2 + 6x + 5} \]
#### Explanation:
1. First, factor each polynomial expression.
- \( x^2 + 2x + 1 \) factors to \( (x + 1)^2 \)
- \( x^2 - 25 \) factors to \( (x + 5)(x - 5) \)
- \( x - 5 \) remains \( x - 5 \)
- \( x^2 + 6x + 5 \) factors to \( (x + 5)(x + 1) \)
2. Substituting the factors back, the expression becomes:
\[
\frac{(x + 1)^2}{x - 5} \times \frac{(x + 5)(x - 5)}{(x + 5)(x + 1)}
\]
3. Simplify the expression:
- Cancel the common factors in the numerator and the denominator.
Simplified form:
\[
\frac{(x + 1) \cdot (x + 1)}{(x - 5)} \times \frac{(x + 5) \cdot (x - 5)}{(x + 5) \cdot (x + 1)}
\]
After canceling out the common factors, we get:
\[
\frac{x + 1}{1} \times \frac{x - 5}{1}
\]
4. Finally, the simplified answer is:
\[
\frac{x + 1}{x + 1} \times \frac{x - 5}{x - 5} = \frac{(x+1).(x-5}{(x-5).(x+5)} = \frac{x+1}{x+5}
]
Note: Make sure to show all steps in your workings and simplify at each step to achieve full marks.
#### Instructions:
Utilize the provided text box to input your multiplication and simplification steps. Upon completion, you may add any supplementary files via "Add a File" or record](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fee316dc0-9fcf-44c0-a9c4-799945d7ab8e%2Fb0f477a9-9967-47fa-a040-466858edbdd6%2Fstvz17j_processed.png&w=3840&q=75)
Transcribed Image Text:### Multiply. Show all work to receive credit for your answer.
\[ \frac{x^2 + 2x + 1}{x - 5} \times \frac{x^2 - 25}{x^2 + 6x + 5} \]
#### Explanation:
1. First, factor each polynomial expression.
- \( x^2 + 2x + 1 \) factors to \( (x + 1)^2 \)
- \( x^2 - 25 \) factors to \( (x + 5)(x - 5) \)
- \( x - 5 \) remains \( x - 5 \)
- \( x^2 + 6x + 5 \) factors to \( (x + 5)(x + 1) \)
2. Substituting the factors back, the expression becomes:
\[
\frac{(x + 1)^2}{x - 5} \times \frac{(x + 5)(x - 5)}{(x + 5)(x + 1)}
\]
3. Simplify the expression:
- Cancel the common factors in the numerator and the denominator.
Simplified form:
\[
\frac{(x + 1) \cdot (x + 1)}{(x - 5)} \times \frac{(x + 5) \cdot (x - 5)}{(x + 5) \cdot (x + 1)}
\]
After canceling out the common factors, we get:
\[
\frac{x + 1}{1} \times \frac{x - 5}{1}
\]
4. Finally, the simplified answer is:
\[
\frac{x + 1}{x + 1} \times \frac{x - 5}{x - 5} = \frac{(x+1).(x-5}{(x-5).(x+5)} = \frac{x+1}{x+5}
]
Note: Make sure to show all steps in your workings and simplify at each step to achieve full marks.
#### Instructions:
Utilize the provided text box to input your multiplication and simplification steps. Upon completion, you may add any supplementary files via "Add a File" or record
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