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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![### Math Practice Exercises
#### Section A
**6. Simplify this expression \( \frac{7!}{(7-2)!} \).**
Options:
- A. 42
- B. 14
- C. 9
- D. 5
Solution:
The expression is given as \( \frac{7!}{(7-2)!} \). Simplifying, we get:
\[ \frac{7!}{5!} = \frac{7 \times 6 \times 5!}{5!} = 7 \times 6 = 42 \]
Correct answer: **A. 42**
#### Section B
**7. Write the equation without fractions:**
\[ \frac{3 + a}{2a} = \frac{1}{3} + \frac{5}{6a} \]
Options:
- A. \( 3 + a = 1 + 5 \)
- B. \( 9 + 3a = 2a + 5 \)
- C. \( 2a = 3 + 6a \)
- D. \( 2a^2 = 3a + 6a^2 \)
Solution:
To write the equation without fractions, we first find a common denominator and then multiply both sides of the equation.
#### Section C
**8. Subtract**
\[ \frac{y}{y^2 - 7y - 18} - \frac{3}{y + 2} \]
Options:
- A. \( \frac{y - 9}{(y - 9)(y + 2)} \)
- B. \( \frac{2y + 7}{(y - 9)(y + 2)} \)
- C. \( \frac{-2y + 27}{(y - 9)(y + 2)} \)
- D. \( \frac{y - 18}{(y - 9)(y + 2)} \)
Solution:
The teacher's notes indicate factoring and combining the fractions:
- Factor \( y^2 - 7y - 18 \) as \( (y - 9)(y + 2) \).
- Obtain a common denominator and subtract the fractions accordingly.
The correct method and detailed solution will be shown to adhere to algebraic rules.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcb9ae157-14d8-4a5d-816a-c898f523ece8%2Ff6862b78-55a7-4141-a2e3-087ec8504ea7%2Flzg036v_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Math Practice Exercises
#### Section A
**6. Simplify this expression \( \frac{7!}{(7-2)!} \).**
Options:
- A. 42
- B. 14
- C. 9
- D. 5
Solution:
The expression is given as \( \frac{7!}{(7-2)!} \). Simplifying, we get:
\[ \frac{7!}{5!} = \frac{7 \times 6 \times 5!}{5!} = 7 \times 6 = 42 \]
Correct answer: **A. 42**
#### Section B
**7. Write the equation without fractions:**
\[ \frac{3 + a}{2a} = \frac{1}{3} + \frac{5}{6a} \]
Options:
- A. \( 3 + a = 1 + 5 \)
- B. \( 9 + 3a = 2a + 5 \)
- C. \( 2a = 3 + 6a \)
- D. \( 2a^2 = 3a + 6a^2 \)
Solution:
To write the equation without fractions, we first find a common denominator and then multiply both sides of the equation.
#### Section C
**8. Subtract**
\[ \frac{y}{y^2 - 7y - 18} - \frac{3}{y + 2} \]
Options:
- A. \( \frac{y - 9}{(y - 9)(y + 2)} \)
- B. \( \frac{2y + 7}{(y - 9)(y + 2)} \)
- C. \( \frac{-2y + 27}{(y - 9)(y + 2)} \)
- D. \( \frac{y - 18}{(y - 9)(y + 2)} \)
Solution:
The teacher's notes indicate factoring and combining the fractions:
- Factor \( y^2 - 7y - 18 \) as \( (y - 9)(y + 2) \).
- Obtain a common denominator and subtract the fractions accordingly.
The correct method and detailed solution will be shown to adhere to algebraic rules.
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