Find the partial fraction decomposition for the rational expressi 6x2- x-13 x(x+ 1)(x- 1) 2. 6x-x-13 %3D x(x+ 1)(x- 1) (Use integers or fractions for any numbers in the expression.)
Find the partial fraction decomposition for the rational expressi 6x2- x-13 x(x+ 1)(x- 1) 2. 6x-x-13 %3D x(x+ 1)(x- 1) (Use integers or fractions for any numbers in the expression.)
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![### Partial Fraction Decomposition for Rational Expressions
**Problem Statement:**
Find the partial fraction decomposition for the rational expression:
\[
\frac{6x^2 - x - 13}{x(x + 1)(x - 1)}
\]
**Solution Setup:**
We need to express the rational expression as a sum of simpler fractions. Decompose the expression as follows:
\[
\frac{6x^2 - x - 13}{x(x + 1)(x - 1)} = \frac{A}{x} + \frac{B}{x+1} + \frac{C}{x-1}
\]
Here, \( A \), \( B \), and \( C \) are constants that need to be determined.
**Instructions:**
- Use integers or fractions for any numbers in the expression.
- Solve for \( A \), \( B \), and \( C \) by multiplying through by the common denominator and matching coefficients.
### Graphs or Diagrams
The problem does not include any graphs or diagrams. The focus is on algebraic manipulation to find the values of \( A \), \( B \), and \( C \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F228397b8-cd0e-4924-bc62-b0b7f3293021%2F7bfb19b3-6e70-4ca2-925d-d987c7b14948%2F9ik9avi_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Partial Fraction Decomposition for Rational Expressions
**Problem Statement:**
Find the partial fraction decomposition for the rational expression:
\[
\frac{6x^2 - x - 13}{x(x + 1)(x - 1)}
\]
**Solution Setup:**
We need to express the rational expression as a sum of simpler fractions. Decompose the expression as follows:
\[
\frac{6x^2 - x - 13}{x(x + 1)(x - 1)} = \frac{A}{x} + \frac{B}{x+1} + \frac{C}{x-1}
\]
Here, \( A \), \( B \), and \( C \) are constants that need to be determined.
**Instructions:**
- Use integers or fractions for any numbers in the expression.
- Solve for \( A \), \( B \), and \( C \) by multiplying through by the common denominator and matching coefficients.
### Graphs or Diagrams
The problem does not include any graphs or diagrams. The focus is on algebraic manipulation to find the values of \( A \), \( B \), and \( C \).
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