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
![**Problem Statement**
Solve the equation \(\frac{C}{g} = \frac{Q + u}{u}\) for \(u\).
**Solution Approach**
To solve for \(u\), follow these steps:
1. Start with the equation:
\[
\frac{C}{g} = \frac{Q + u}{u}
\]
2. Cross-multiply to eliminate the fractions:
\[
C \cdot u = g \cdot (Q + u)
\]
3. Distribute \(g\) on the right side:
\[
C \cdot u = g \cdot Q + g \cdot u
\]
4. Move all terms involving \(u\) to one side:
\[
C \cdot u - g \cdot u = g \cdot Q
\]
5. Factor out \(u\):
\[
u \cdot (C - g) = g \cdot Q
\]
6. Solve for \(u\):
\[
u = \frac{g \cdot Q}{C - g}
\]
**Final Solution**
\[
u = \frac{g \cdot Q}{C - g}
\]
**Note:** Ensure \(C \neq g\) to avoid division by zero.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F25dd1725-4fb5-448b-bc71-f1fb53ccdf21%2F53596670-9960-490f-93f6-f5694512310b%2F3kzkm4n_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement**
Solve the equation \(\frac{C}{g} = \frac{Q + u}{u}\) for \(u\).
**Solution Approach**
To solve for \(u\), follow these steps:
1. Start with the equation:
\[
\frac{C}{g} = \frac{Q + u}{u}
\]
2. Cross-multiply to eliminate the fractions:
\[
C \cdot u = g \cdot (Q + u)
\]
3. Distribute \(g\) on the right side:
\[
C \cdot u = g \cdot Q + g \cdot u
\]
4. Move all terms involving \(u\) to one side:
\[
C \cdot u - g \cdot u = g \cdot Q
\]
5. Factor out \(u\):
\[
u \cdot (C - g) = g \cdot Q
\]
6. Solve for \(u\):
\[
u = \frac{g \cdot Q}{C - g}
\]
**Final Solution**
\[
u = \frac{g \cdot Q}{C - g}
\]
**Note:** Ensure \(C \neq g\) to avoid division by zero.
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