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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![The equation in the image is as follows:
\[
\frac{14}{x-3} + \frac{10}{x+6} = 3
\]
This equation consists of two fractional terms added together and set equal to 3. The first term has a numerator of 14 and a denominator of \(x - 3\). The second term has a numerator of 10 and a denominator of \(x + 6\).
### Explanation of Components:
1. **Fractional Terms:**
- The fractions represent rational expressions that depend on the variable \(x\).
- The denominators, \(x - 3\) and \(x + 6\), indicate how each part varies with changes in \(x\).
2. **Equation:**
- The entire expression is set equal to 3, suggesting a potential solution or value for \(x\) such that the sum of the fractions equals 3.
### Educational Context:
This type of equation might appear in algebra courses focusing on solving rational equations. In solving such equations, one looks for values of \(x\) that satisfy the equality, taking into account any restrictions (such as values that make the denominators zero).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa3456819-528d-42b3-b255-e8873e975f3d%2Fb45b48b4-9438-426f-a3d3-0050bd1e7eab%2Fz085ptl_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The equation in the image is as follows:
\[
\frac{14}{x-3} + \frac{10}{x+6} = 3
\]
This equation consists of two fractional terms added together and set equal to 3. The first term has a numerator of 14 and a denominator of \(x - 3\). The second term has a numerator of 10 and a denominator of \(x + 6\).
### Explanation of Components:
1. **Fractional Terms:**
- The fractions represent rational expressions that depend on the variable \(x\).
- The denominators, \(x - 3\) and \(x + 6\), indicate how each part varies with changes in \(x\).
2. **Equation:**
- The entire expression is set equal to 3, suggesting a potential solution or value for \(x\) such that the sum of the fractions equals 3.
### Educational Context:
This type of equation might appear in algebra courses focusing on solving rational equations. In solving such equations, one looks for values of \(x\) that satisfy the equality, taking into account any restrictions (such as values that make the denominators zero).
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