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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Equations and Inequations
Equations and inequalities describe the relationship between two mathematical expressions.
Linear Functions
A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.
Question
![**Solving Rational Equations**
To solve the equation, please refer to Example 3 for similar problems.
**Equation:**
\[ \frac{1}{3x + 6} = \frac{x - 2}{3} + \frac{x - 1}{3x + 6} \]
**Solutions:**
\( x = \_\_\_\_\_ \) (smaller value)
\( x = \_\_\_\_\_ \) (larger value)
In this problem, you are tasked with solving a rational equation. Rational equations are equations that contain fractions whose numerators and/or denominators are polynomials. Simplifying and solving these equations often involves finding a common denominator or multiplying through by the least common multiple to clear the fractions.
### Steps to Solve:
1. Identify the common denominator for all terms.
2. Multiply through by the common denominator to eliminate the fractions.
3. Solve the resulting polynomial equation.
4. Check your answers in the original equation to avoid extraneous solutions.
In this specific equation:
- The common denominator would be \(3(3x + 6)\).
- Multiply each term by this common denominator.
- Solve the resulting linear equation.
Please attempt the problem and refer to Example 3 for detailed step-by-step guidance.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc60d0879-bf1d-4600-af9d-cdd728ad041f%2F01bb78be-2457-4ca8-8d81-499d1f3a617b%2Fqcdarqf_processed.png&w=3840&q=75)
Transcribed Image Text:**Solving Rational Equations**
To solve the equation, please refer to Example 3 for similar problems.
**Equation:**
\[ \frac{1}{3x + 6} = \frac{x - 2}{3} + \frac{x - 1}{3x + 6} \]
**Solutions:**
\( x = \_\_\_\_\_ \) (smaller value)
\( x = \_\_\_\_\_ \) (larger value)
In this problem, you are tasked with solving a rational equation. Rational equations are equations that contain fractions whose numerators and/or denominators are polynomials. Simplifying and solving these equations often involves finding a common denominator or multiplying through by the least common multiple to clear the fractions.
### Steps to Solve:
1. Identify the common denominator for all terms.
2. Multiply through by the common denominator to eliminate the fractions.
3. Solve the resulting polynomial equation.
4. Check your answers in the original equation to avoid extraneous solutions.
In this specific equation:
- The common denominator would be \(3(3x + 6)\).
- Multiply each term by this common denominator.
- Solve the resulting linear equation.
Please attempt the problem and refer to Example 3 for detailed step-by-step guidance.
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