Concept explainers
To write:The partial fraction decomposition of the rational expression
Answer to Problem 20E
Explanation of Solution
Given:
Calculation:
The given rational expression is
The factor of the denominator is given by
So, the rational expression becomes
The form of partial fraction decomposition of this expression is given by
On simplifying
Now, compare the coefficient of x ,
And comparing the constant term on both sides
Solving equations
Therefore, using equation
Therefore, the partial fraction decomposition is given by
In order to check the result algebraically, simplify the expression on right hand side of the equation
This resultant expression is same as the given rational expression. Hence, the partial fraction of the given expression is true.
Chapter 7 Solutions
EBK PRECALCULUS W/LIMITS
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning