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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![### Assessment: End of Unit - Question 4
**Instructions:**
**Objective:** Find all values of \( x \) that make the equation true.
\[
\frac{3}{x-4} = \frac{x-5}{x}
\]
**Note:** You must show all work to get credit for this question.
**Content:**
- **Equation to Solve:** \(\frac{3}{x-4} = \frac{x-5}{x}\)
- **Steps Required:**
1. **Cross-multiply** to eliminate the fractions:
\[
3x = (x-4)(x-5)
\]
2. **Expand the right-hand side** and simplify the equation.
3. **Find the values of \( x \)** that satisfy the equation.
4. **Verify** if there are any restrictions or invalid solutions (such as values making the denominator zero).
- **Result:** The correct values of \( x \) must be computed and the process clearly detailed to receive full credit.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F608fb8d0-89b6-408a-87ea-057ba2e1c226%2F4b564161-ce8c-485e-a5b1-23f26d5375e4%2F8rdmt9_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Assessment: End of Unit - Question 4
**Instructions:**
**Objective:** Find all values of \( x \) that make the equation true.
\[
\frac{3}{x-4} = \frac{x-5}{x}
\]
**Note:** You must show all work to get credit for this question.
**Content:**
- **Equation to Solve:** \(\frac{3}{x-4} = \frac{x-5}{x}\)
- **Steps Required:**
1. **Cross-multiply** to eliminate the fractions:
\[
3x = (x-4)(x-5)
\]
2. **Expand the right-hand side** and simplify the equation.
3. **Find the values of \( x \)** that satisfy the equation.
4. **Verify** if there are any restrictions or invalid solutions (such as values making the denominator zero).
- **Result:** The correct values of \( x \) must be computed and the process clearly detailed to receive full credit.
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