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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Question
![The expression given is:
\[
\frac{5}{(x-1)(x+4)} \quad \text{(shape: } \frac{a}{x-1} + \frac{b}{x+4} \text{)}
\]
This mathematical expression represents a rational function with a shape that can be rewritten using partial fraction decomposition. The goal is to express the fraction \(\frac{5}{(x-1)(x+4)}\) as the sum of two simpler fractions, \(\frac{a}{x-1}\) and \(\frac{b}{x+4}\), where \(a\) and \(b\) are constants to be determined.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fccac55ee-732b-4607-a38e-f5bd0a8aacb2%2F352fbdf4-28a2-4886-bf3b-dce63986189e%2Fgq6mys_processed.png&w=3840&q=75)
Transcribed Image Text:The expression given is:
\[
\frac{5}{(x-1)(x+4)} \quad \text{(shape: } \frac{a}{x-1} + \frac{b}{x+4} \text{)}
\]
This mathematical expression represents a rational function with a shape that can be rewritten using partial fraction decomposition. The goal is to express the fraction \(\frac{5}{(x-1)(x+4)}\) as the sum of two simpler fractions, \(\frac{a}{x-1}\) and \(\frac{b}{x+4}\), where \(a\) and \(b\) are constants to be determined.
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