Concept explainers
To calculate:
Write the partial fraction decomposition of the rational expression. Use a graphing utility to check your result.
Answer to Problem 58E
The partial fraction decomposition is
Explanation of Solution
Given information:
The given equation is
Calculation:
Since the degree of numerator is not less than degree of the denominator we need to do polynomial long division which is as follows.
Now, let us deal with
Factor the denominator:
The form of the partial fraction decomposition is
Write the right-hand side as a single fraction.
The denominators are equal, so we require the equality of the numerators:
Expand the right hand side:
Collect up the like terms:
The coefficients near the like terms should be equal, so the following system is obtained:
By solving it we get,
Therefore,
Conclusion:
The partial fraction decomposition is
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