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
It's a rational expression you divide the top fraction by the bottom
![### Division of Rational Expressions
To divide the given rational expressions, follow these steps:
#### Problem:
\[
\frac{x^2 + 10x + 25}{x^2 - 25} \div \frac{x^2 - 2x - 35}{x^2 - 12x + 35}
\]
#### Method:
1. **Rewrite as Multiplication**:
To divide fractions, multiply by the reciprocal of the divisor.
\[
\frac{x^2 + 10x + 25}{x^2 - 25} \times \frac{x^2 - 12x + 35}{x^2 - 2x - 35}
\]
2. **Factor Each Quadratic Expression**:
**Numerator of the First Fraction:**
\[
x^2 + 10x + 25 = (x + 5)(x + 5)
\]
**Denominator of the First Fraction:**
\[
x^2 - 25 = (x + 5)(x - 5)
\]
**Numerator of the Second Fraction:**
\[
x^2 - 12x + 35 = (x - 7)(x - 5)
\]
**Denominator of the Second Fraction:**
\[
x^2 - 2x - 35 = (x - 7)(x + 5)
\]
3. **Substitute the Factors Back**:
\[
\frac{(x + 5)(x + 5)}{(x + 5)(x - 5)} \times \frac{(x - 7)(x - 5)}{(x - 7)(x + 5)}
\]
4. **Cancel Common Factors**:
After canceling common factors, the expression simplifies to:
\[
\frac{(x + 5)}{(x - 5)}
\]
5. **Simplify Your Answer:**
The simplified expression is:
\[
\frac{x + 5}{x - 5}
\]
Remember, always check for values that make the original denominators zero to identify any restrictions on the variables.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6c693121-0c53-4461-96bf-03d77f2fd62b%2F00339f94-987f-41ca-a24d-fb4b3d79fd7a%2Fq1vz7em_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Division of Rational Expressions
To divide the given rational expressions, follow these steps:
#### Problem:
\[
\frac{x^2 + 10x + 25}{x^2 - 25} \div \frac{x^2 - 2x - 35}{x^2 - 12x + 35}
\]
#### Method:
1. **Rewrite as Multiplication**:
To divide fractions, multiply by the reciprocal of the divisor.
\[
\frac{x^2 + 10x + 25}{x^2 - 25} \times \frac{x^2 - 12x + 35}{x^2 - 2x - 35}
\]
2. **Factor Each Quadratic Expression**:
**Numerator of the First Fraction:**
\[
x^2 + 10x + 25 = (x + 5)(x + 5)
\]
**Denominator of the First Fraction:**
\[
x^2 - 25 = (x + 5)(x - 5)
\]
**Numerator of the Second Fraction:**
\[
x^2 - 12x + 35 = (x - 7)(x - 5)
\]
**Denominator of the Second Fraction:**
\[
x^2 - 2x - 35 = (x - 7)(x + 5)
\]
3. **Substitute the Factors Back**:
\[
\frac{(x + 5)(x + 5)}{(x + 5)(x - 5)} \times \frac{(x - 7)(x - 5)}{(x - 7)(x + 5)}
\]
4. **Cancel Common Factors**:
After canceling common factors, the expression simplifies to:
\[
\frac{(x + 5)}{(x - 5)}
\]
5. **Simplify Your Answer:**
The simplified expression is:
\[
\frac{x + 5}{x - 5}
\]
Remember, always check for values that make the original denominators zero to identify any restrictions on the variables.
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