Let f(x) = and g(x) = - Find and simplify: (f + g)(x) Select one: A. x²+3x-1 x(x-1) B. -x+3x+1 x(x-1) C. x²+3x-1 x²-1 D. -x²+3x-l x²-1 E. x²-3x-1 x(x-1) 1-x
Let f(x) = and g(x) = - Find and simplify: (f + g)(x) Select one: A. x²+3x-1 x(x-1) B. -x+3x+1 x(x-1) C. x²+3x-1 x²-1 D. -x²+3x-l x²-1 E. x²-3x-1 x(x-1) 1-x
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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Question
![**Mathematics: Functions and Simplification**
---
**Problem Statement:**
Let \( f(x) = \frac{1}{x-1} \) and \( g(x) = \frac{1-x}{x} \).
Find and simplify: \( (f + g)(x) \).
**Multiple Choice Options:**
Select one:
A. \( \frac{x^2 + 3x - 1}{x(x-1)} \)
B. \( \frac{-x^2 + 3x + 1}{x(x-1)} \)
C. \( \frac{x^2 + 3x - 1}{x - 1} \)
D. \( \frac{-x^2 + 3x + 1}{x - 1} \)
E. \( \frac{x^2 - 3x - 1}{x(x-1)} \)
---
**Notes on Function Simplification:**
1. **Function Definitions:**
- \( f(x) = \frac{1}{x-1} \)
- \( g(x) = \frac{1-x}{x} \)
2. **Combining Functions:**
To find \( (f + g)(x) \), add the two functions together:
\[
(f + g)(x) = f(x) + g(x) = \frac{1}{x-1} + \frac{1-x}{x}
\]
3. **Simplification Steps:**
- Find a common denominator for the two fractions.
- Combine and simplify the fractions.
This exercise helps students practice combining fractions with different denominators and simplifying rational functions.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F16026111-938d-475f-a906-01f519f5a5a9%2F1dc93e7f-8c2e-449f-b565-9ee980b731bf%2F718a8w_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Mathematics: Functions and Simplification**
---
**Problem Statement:**
Let \( f(x) = \frac{1}{x-1} \) and \( g(x) = \frac{1-x}{x} \).
Find and simplify: \( (f + g)(x) \).
**Multiple Choice Options:**
Select one:
A. \( \frac{x^2 + 3x - 1}{x(x-1)} \)
B. \( \frac{-x^2 + 3x + 1}{x(x-1)} \)
C. \( \frac{x^2 + 3x - 1}{x - 1} \)
D. \( \frac{-x^2 + 3x + 1}{x - 1} \)
E. \( \frac{x^2 - 3x - 1}{x(x-1)} \)
---
**Notes on Function Simplification:**
1. **Function Definitions:**
- \( f(x) = \frac{1}{x-1} \)
- \( g(x) = \frac{1-x}{x} \)
2. **Combining Functions:**
To find \( (f + g)(x) \), add the two functions together:
\[
(f + g)(x) = f(x) + g(x) = \frac{1}{x-1} + \frac{1-x}{x}
\]
3. **Simplification Steps:**
- Find a common denominator for the two fractions.
- Combine and simplify the fractions.
This exercise helps students practice combining fractions with different denominators and simplifying rational functions.
![### Problem Statement
Consider the functions:
\[ f(x) = \frac{1}{x-1} \]
\[ g(x) = \frac{1-x}{x} \]
Find and simplify the expression:
\[ \left(\frac{g}{f}\right)(x) \]
### Multiple Choice Options
Select one:
- **A.** \(-1\)
- **B.** \(\frac{(x-1)^2}{x}\)
- **C.** \(\frac{1}{x}\)
- **D.** \(\frac{(x-1)^2}{x}\)
- **E.** \(-\frac{1}{x}\)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F16026111-938d-475f-a906-01f519f5a5a9%2F1dc93e7f-8c2e-449f-b565-9ee980b731bf%2F8oewatr_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Problem Statement
Consider the functions:
\[ f(x) = \frac{1}{x-1} \]
\[ g(x) = \frac{1-x}{x} \]
Find and simplify the expression:
\[ \left(\frac{g}{f}\right)(x) \]
### Multiple Choice Options
Select one:
- **A.** \(-1\)
- **B.** \(\frac{(x-1)^2}{x}\)
- **C.** \(\frac{1}{x}\)
- **D.** \(\frac{(x-1)^2}{x}\)
- **E.** \(-\frac{1}{x}\)
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